Cook the quinoa: Place quinoa in a fine mesh strainer and rinse well under cold running water; drain and set aside. Bring 1 cup of water to a boil in a small saucepan. Add the quinoa, reduce the heat to a low simmer, cover, and cook for 12-15 minutes, until water is absorbed. Let quinoa cool for at least 15 minutes.*
Place the oats in the bowl of a food processor and process until they are ground up semi-finely. It is ok if a few larger bits remain.
To the oats in the food processor, add the cooked quinoa, panko breadcrumbs, garlic, egg, ketchup, paprika, garlic powder, onion powder, salt and black pepper. Pulse about 8 times to begin to mix the ingredients. Add the corn, bell pepper and green onions and pulse 6-8 more times to combine.
Divide the mixture into 4 equal portions and then shape each portion into a burger patty that is about ½-inch thick.
To cook on the stove: Heat about 1 tablespoon of olive oil in a cast iron skillet, nonstick skillet or grill pan over medium heat. Cook the veggie burgers in the hot pan for 4-6 minutes per side, or until the burgers are browned on the outside and reach at least 160° F in the center. If you find that the outside is browning too much before the inside cooks through, you can cover the pan to trap the heat.
To cook in the oven: Preheat oven to 375° F. Place burgers on a parchment paper-lined baking sheet. Bake for 13-15 minutes, flipping burgers over halfway through the cook time. Burgers are done when the center registers at least 160° F on an instant read thermometer.
To cook on an outdoor grill: Make sure the grill grates are clean and preheat a gas or charcoal grill to medium heat. Oil the grill grates well and cook burgers for 4-6 minutes per side, until burgers reach at least 160° F in the center. You may wish to use a grill topper or grill basket to ensure that the burgers hold their shape, as they can be more delicate than meat burgers.
Serve veggie burgers on burger buns with toppings, as desired.