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Decrease Gravity

Explanation:
The water droplets we experience on earth are mostly so small because of gravity: when a water droplet becomes too big, gravity rips it apart before it can get bigger (like when you're not quite closing a tap, the only reason it doesn't get bigger is because the mass of the droplet is bigger than the force "gluing" the water to the tap).

So when you decrease the gravity, the droplets in the clouds can get bigger without raining down on your planet. The reason why water can even stay up in clouds is because the mass of a water droplet increases by the $frac{4}3cdot picdot d^3$ of its diameter while the surface only by $pi cdot d^2$. (d = diameter), so at some point the mass and volume has decreased so much that the updraft from the air is enough. Here you can see how the blue line($frac{4}3cdot picdot d^3$) is increasing faster than orange line ($ pi cdot d^2$)

Which is why less gravity is key.

Pollution will do the trick for you.

For the record, Brazil has the largest raindrops on Earth, in its northern region - right where people burn a soccer field area worth of forest per day to make room for farming lands. Some scientists such as Peter Hobbs think that the smoke causes water to condense onto raindrops of up to 1 centimeter in length.

Source: Geophyisical Research Letters, Volume 31, issue 13

Everywhere else on Earth, raindrops tend to split if they grow larger than 4 or 5 millimeters.

The upper size of raindrops is set by the strength of surface tension compared to the forces that batter them, mostly wind due to falling(*). This is hard to scale up indefinitely, so under terrestrial conditions they will likely remain less than 8.8 mm.

Another solution is to do something like Hal Clement's classic sf novel Close to critical (1964) where the atmosphere is mostly water close to the critical point: during night water droplets several meters in size condense out and fall slowly (since the density of the droplets is close to the "air"). This might be a bit too alien for you, since it requires a high-temperature high-pressure atmosphere. But it does have huge droplets.

(* If the droplet has radius $r$ the total surface tension energy is $E=4pigamma r^2$. If it falls at terminal velocity the drag force is equal to the gravitational force, and we can guess that the wind shaking it will have a force of the same size $Fapprox (4pi g rho/3) r^3$. Here we assume zero density air; thicker air like the Clement story would use $rho_{fluid}-rho_{air}$. To split the droplet this force has to work along the distance $2r$ to overcome the surface tension energy, giving us $F(2r)=(8pi g rho/3) r^4=E$, or $rapprox sqrt{ 3 gamma / 2g rho }$. So unless water becomes lighter or gets a higher surface tension the only way of increasing the droplet size is to lower gravity. And the effect looks relatively minor.)

Rain drops form in the upper atmosphere when air humidity condenses around condensation nuclei.

As soon as their weight overcomes the sum of buoyancy and updraft, they fall down to the ground.

Here is the trick for you to increase the droplet size. You cannot substantially increase the buoyancy, but if you have stronger updraft, due to a stronger ascending current, the droplets will have to grow bigger before their weight is great enough to fall.

This is a version on steroids of what already happens on Earth: low clouds in calm air result in a fine mist or drizzle, while cumulonimbus with strong winds give bigger drops.

If you thicken the atmosphere you will get the effects you are looking for. Increase the Troposphere from the Earth normal ~12km average to 18 or 24km thick. This won't materially change the surface conditions but will greatly increase the amount of weather that can happen above you. If you have ever encountered monsoon conditions then you know how much heavier tropical rain can be where the Troposphere is thicker compared to temperate or Artic rain where the Troposphere is thinner.

---- Update ----

According to the USGS (https://water.usgs.gov/edu/raindropsizes.html ) raindrop size is directly related to the number of other raindrops encountered, with an upper limit in earth normal conditions of around 5mm. A thicker atmosphere encourages more encounters and hence larger raindrops. A typical 'soft' Irish day may have drops of 0.1mm or smaller; you are not aware of being rained on, just the feeling of becoming increasingly damp. Contrast that with an Equatorial coastal Monsoon burst where drops of 5mm or more will physically hurt you as they strike.

Without going into details (most of which are already covered by other posts in depth) You would want a combination of decreased gravity, increased updrafts, and increased water surface tension. Each individually could be relatively small changes, but when acting together they may provide the cumulative effect you're looking for.

'Invent' a trace element that makes water have a higher surface tension, or make the water molecules stick more to each other because of the trace element.

The element will likely have to blow up from the planet surface, like dessert dust blows into clouds on our planet, which in turn allows you to design where the rain will have the bigger drops. You can select a smaller area or a bigger area, or even planet wide, by describing where the dust ends up. Or you can leave it open to the readers to work it out.

It is also open to you whether the element still works when the rain has hit the surface. If you let it sink faster than the water you can have the surface of the water normal.

If such an element is not known on earth it can still be on your planet.