I put the garlic first by itself because I like to "tame" it.  I separate a head of garlic into cloves but don't bother peeling them.  I place them in the microwave, scattered on the rotating plate, and zap them full power until they start 'popping' (in mine, it's 20-40 seconds until this happens), wait a few more seconds (only a few), and pull them out.  The skins will be loose and opened, and you can pop them off easily.  Then I put them through the garlic press, and the result is richly nutty garlicky  but not bitter or biting; it's as tamed as if it was roasted in the oven without heating up the whole oven.  You can also peel them raw and slice and dice if you prefer knife work & sharp, biting garlic to lazy zap & pressed mellow garlic.

Then start with olive oil (and a little butter too if you like) and saute the onions....depending on my mood sometimes heat them gently until they're just barely getting translucent and soft but still pale; sometimes I do it over higher heat to brown their edges; sometimes I go for carmelized.  Remember they're going to be cooked more with everything else.  Add the garlic along with the tomatoes in the next step.

Then add the tomatoes, stir until they’re softening and releasing a lot of liquid.  Add the squash, eggplant if using, and peppers, and stir more until they get a touch browned for more flavor in the final dish.

Add the corn and stock or a bit of water to cover the vegetables, simmer a few minutes, stir in the herbs, pine nuts if using; correct seasonings, salt, pepper, and enjoy.