Preheat oven to 375F (190C). Line a cookie sheet with parchment paper, or spray with nonstick spray.
Place everything except the flour in the bowl of a food processor and blend until almost smooth and only small flecks of vegetables remain (I like my burgers fairly homogenous; if you prefer chunkier burgers, process a bit less). Sprinkle with 1/4 cup (60 ml) flour to start, and pulse to combine; check the texture of the mixture with your hands. It should be very moist but still hold together. If the mixture is too wet, add more flour until desired consistency is reached.
Shape the mixture into 6-8 burgers, depending on how big you’d like them. Flatten each burger to 1/2 inch (2.5 cm) thickness and place on the cookie sheet, spacing evenly (these won’t spread as they bake).
Bake about 15 minutes on one side, then flip and bake another 10-15 minutes on the other side, until burgers are lightly browned. These may also be cooked on a flat grill; spray with olive oil spray and grill 8-10 minutes on one side, then flip and grill another 5-8 minutes on the other side.