Put 2 tablespoons of the olive oil in a deep nonstick or cast-iron skillet with a lid over medium heat. Put the onion, garlic, and chile in a food processor and pulse a few times to grind almost smooth. Add the mixture to the pan with a sprinkle of salt and pepper and cook and stir.

Stir the zucchini into the onion mixture along with 1/2 cup of the corn and another sprinkle of salt and pepper. Put the remaining corn into a food processor and let the machine run until it becomes a thick paste. Continue to cook and stir the zucchini mixture until the vegetables release all their water and it starts to evaporate, about 5 minutes. Stir in the corn paste and the cornmeal. Remove from the heat, cover, and let rest for 10 minutes. If the mixture seems too wet, stir in a little flour to help bind it. Taste and adjust the seasoning.

Form 4 to 6 patties and let sit for a few minutes if you have time. (You can make the burger mixture or even shape the burgers up to several hours in advance. Just cover tightly and refrigerate, then bring everything back to room temperature before cooking.) Wipe out the pan, put in the remaining 2 tablespoons of oil, and turn the heat to medium. A minute later, add the patties. Cook until nicely browned on one side, about 5 minutes; turn carefully and cook on the other side until firm and browned.

Serve on plates with the same sorts of side dishes you'd use for simply prepared meats or on buns with the usual burger fixings. Or cool and refrigerate or freeze for later use.