Heat a grill to medium-high. Place the corn and bell pepper directly on the grill and cook until charred on the outside, 2-3 minutes per side. Remove and set aside until cool enough to handle.
When cooled, cut the corn kernels off the cob. Remove the seeds from the pepper and cilantro. Chop the flesh into 1-inch pieces.
Add the onion, carrot, and garlic to the bowl of a food processor fitted with the steel blade. Pulse until ground and no large chunks remain, 10-15 pulses. Reserve ½ cup of the beans and add the remaining to the food processor along with the corn and bell pepper. Process again until a dough starts to form. Transfer to a mixing bowl.
Pour the oats and sunflower seeds into the food processor and pulse until ground into a flour. Add to the bowl along with the remaining beans, quinoa, spices, salt, and pepper. Add the flax egg and stir to combine. Add 3 tablespoons ground flaxseed and stir to combine. Add another tablespoon of ground flaxseed, if needed, to help the mixture bind.
Shape into 6 burgers of equal size. Place on a parchment-lined baking sheet and refrigerate for at least 1 hour.
Preheat the oven to 400ºF. Bake the burgers on the center rack for 25-30 minutes, flipping halfway through. Let cool for 5 minutes to firm up before serving. Top as you prefer and enjoy!
Notes
To make a flax egg, mix 1 tablespoon ground flaxseed with 3 tablespoons water and set aside for 5 minutes.