Currently, I prepare onions to put on a pizza by using a food processor to chop them, then strain them and let them dry. Then, I put them in containers before use.
However, the onions have been too moist lately, and make the pizzas soggy when they're put on them. How can I remove some of the moisture so they don't do that?
One technique for removing water from a vegetable, which works very well for onions, is to salt them liberally. Then give them some time to sit, preferably in a shallow layer.
The salt will extract water from the vegetable, due to the osmotic gradient between the salt outside and the vegetable inside. Some of the salt will go into the vegetable, but much will remain outside; you'll need to figure out how much salt you can get away with using before your vegetable is too salty, but it's typically a large amount in my experience.
Once enough water has been extracted, rinse the vegetable off (to remove the excess salt), and pat it dry between two parts of a towel (or two paper towels). The vegetable will now have much less moisture in it, which will both lead to crispier and quicker frying, and less moisture coming out in the cooking process.
A second option, in your specific case, is to store them in open containers. The refrigerator will dry the onions out over time. This is usually a bad thing, and you intentionally close containers to prevent this; but in your case, depending on the length of time you're talking about, it could be a good thing. I wouldn't do this for more than a few days (as it will really dry the onion), but it might be worth testing to see if it helps. This may leave your refrigerator (and its contents) smelling like onions, of course.
Alternately, you can store the onion on a mesh or grate which allows moisture to slip down below the onion; it may help prevent some moisture re-absorption and improve your results.
Or you could try saute em before hand then just drop em on few minutes before your pizza is done?
I do this a lot for making onion bhajis. Top and tail onions, peel and slice thinly. Place in large bowl, separate with your fingers, then add about 1/2 teaspoon of salt per onion. Mix together and leave for at least 2 hours. Rinse to remove excess salt. Drain through a sieve. Lay a large piece of cheesecloth, or a tea towel on the work surface. Place onions in a strip in the middle. Roll into a sausage. Twist both ends in opposite directions, this will release a lot of the water. Don't overdo it or the onions will break up.
You could, of course, actively dry them, in a food dehydrator or one of the many improvised versions of the same thing. You don't need to completely dehydrate them (unless, as @mrog does, you find that you like that) though if you do you can skip refrigeration. I often partially dry apples when making apple pie to get the "pie juice" thicker without resorting to corn starch or tapioca. I also mix fully dried apples with normal apples. I see no reason that the same techniques should not apply to onions and pizzas.
That would be easier with sliced rings rather than diced/chopped onion, which will tend to clump and probably be difficult to dry. I guess mixing purchased dried onion or garlic with the diced/chopped onion might work, if rings are not an option.
The most effective way to remove the moisture from onions is through stir-frying, which is an experience I've gained after years of experimentation in the kitchen. Put the sliced onions into a preheated pan and quickly stir-fry them over high heat for 3 - 4 minutes. Keep stirring constantly during this period to prevent burning. When you see the onions turn transparent, turn to medium-low heat and continue stir-frying until they turn golden brown. By then, the moisture will naturally evaporate. If you want an easier way, the pickling method is also a good option. Sprinkle an appropriate amount of salt on the sliced onions and let them sit for 15 - 20 minutes. Then use kitchen paper to dry the separated moisture. This method is especially suitable for making salads and burger toppings. It can not only maintain the crisp and tender texture of the onions but also avoid having excess moisture affect other ingredients.
