The first thing you do is cut the plants back to about 3 or 4 nodes and
harvest the tops, this will make them put 2x as many top branches.
Take the harvested basil and put it in a collander and spray the hell
out of it with the sink sprayer to remove the aphids ( which by now are
basil flavored anyway) and use it. If you are not ready top use it pack
it into an ice cube tray and add water and freeze until you are ready.
Now take the plant and set the sink spray for warm and hose down the
plant and you will remove most of the aphids.
This is something you can repeat every 4 days or so, you are
controlling the aphids by washing them down the drain not poisoning
anything.
Aphids like lush new growth the best, are you feeding your potted
plants heavily?