Heat olive oil in a medium skillet over medium-low heat. Add garlic, onion, and diced veggies and cook for about 10 minutes, or until softened and fragrant.
Combine all ingredients in a food processor and pulse until well combined (alternatively, may can mash everything together in a large bowl). Scoop the mixture into 6-8 mounds (depending on desired size) on a plate, then use your hands to press and shape them into patties (if the mixture is a bit sticky, you may refrigerate it for 30 minutes to firm up, then form it into patties).
Preheat oven to 375 degrees F. Cook the patties in a skillet that has been lightly coated with oil over medium heat until lightly browned, about 4 minutes per side. Transfer the patties to a sheet pan (or use your skillet pan if it is oven-safe) to bake for 10-20 minutes, or until your desired firmness is reached.