Thinly slice 1 small red onion into rings, then pop the rings apart so they’re not attached. Toss onion rings, 1/2 cup red wine vinegar, 2 tablespoons extra-virgin olive oil, 1 teaspoon oregano, and 1/4 teaspoon salt in a large bowl and leave at room temperature while you cook. If possible, do this the night before, the onions get more delicious and turn hot pink with more time! Store any leftovers in a sealed container in the refrigerator. They keep in the refrigerator for up to 2 weeks.
Combine 1 pound chicken sausage (see NOTES below if you can only find ground chicken), 1 large, grated zucchini (about 1 1/2 cups grated), 1/3 cup breadcrumbs, 1 large egg yolk, 1/4 cup chopped basil, 2 tablespoons chopped mint, and 1/2 teaspoon salt in a large bowl. Use your hands to combine the mixture.
Refrigerate the patties for at least 30 minutes, or freeze for 10 minutes to firm them up before grilling.
Preheat an outdoor grill to 450°F. (See notes below for how to cook indoors).
Divide mixture into four patties. Grab one of your burger buns for reference, and make your patties slightly larger than the buns. They’ll shrink when you cook them and become the perfect size.
Spray both sides of the burgers with non-stick cooking spray, then place on the grill (see NOTES for indoor cooking instructions!). Cook for 6 minutes. If the burger does not release easily from the grill grate after 6 minutes, give it another minute. It should not stick if it’s ready to flip.
Meanwhile, smear mayonnaise all over both sides of the burger buns.
Flip burger and cook for 3 minutes. Add mozzarella to each burger, then close the grill and continue cooking for 3 additional minutes.
Add burger buns to the grill, cut side down, during the last 1 minute of cooking to toast.
Serve the burgers on the buns with marinated red onions.