Preheat the oven to 400F. Arrange the garbanzo beans, carrot, onion, and beet on a baking sheet. Drizzle with olive oil and sprinkle with salt. Roast the vegetables for 20-30 minutes until browned and wilted. Let the veggies cool slightly, then proceed with the rest of the recipe.
Add the roasted vegetables and all remaining ingredients to the bowl of a food processor, and sprinkle with salt. Pulse the mixture several times until the veggies break down and the mixture starts to come together at about the same consistency as rice. When the mixture is evenly chopped, make 3-4 patties, pressing firmly as you go.
Chill patties for 10 minutes in the refrigerator or until ready to use.
To cook, heat a pan with olive oil to medium-high heat. Carefully add the veggie patties. Cook for about 7 minutes on each side, using a big spatula to flip the burgers, until browned and crispy at the edges.
Serve the burgers any way you like. Enjoy!