Combine garbanzo beans, red peppers and caramelized onions, garlic spread, salt, and arugula in large food processor and pulse until finely chopped and almost paste-like.
Transfer to a large bowl and add breadcrumbs. Stir well to combine.
Add egg and mix in well.
Using 1/3 or 1/2 cup measuring cup (depending on how large you want your patties), scoop out burger mixture and form into patties. You want them to be an even thickness from edge to middle.
In large skillet, heat 2 tbsp canola oil over medium-high heat.
Add veggie burgers, working in batches of 2-3 at a time depending on how large your skillet is.
Cook 5 minutes on each side, until they are golden brown.
If you are cooking them to grill for later, let them cool completely and store in airtight container in the refrigerator. To grill: place on oiled grill and cook ~3 minutes on each side, just so they are warm throughout. You can also toast your buns on the grill while you are grilling the burgers.
If you are cooking them to eat now, toast your buns in the oven or on stovetop while you are cooking them.
Spread buns with Olive, Parmesan, and Garlic Everything Spread, then top with burgers, arugula, and feta.