1. Prepare patties: In a large skillet on medium, heat oil. Add onion, season with ⅛ tsp salt and cook, stirring occasionally, until onions are very tender and beginning to lightly caramelize, about 6 minutes. Add garlic, oregano and cumin; sauté 1 minute. Transfer to a food processor and add beans, chipotle and adobo. Pulse until mixture is chopped finely and well combined (do not overprocess).
2. Grate beets into a large bowl on the large holes of a box grater. Squeeze in paper towels thoroughly to remove excess liquid. Add quinoa, bean mixture and egg; stir well. Fold in flour, remaining ¾ tsp salt and pepper. Cover and refrigerate for 2 hours.
3. Preheat oven to 350ºF; line a large baking sheet with parchment paper. Divide bean mixture into 8 portions; form each into a½-inch-thick patty, about 3½ inches wide. Bake on sheet for 15 minutes; carefully turn over and bake 15 minutes longer. Let burgers cool on sheet until they firm up.
4. Grill patties on a greased grill on medium-high until cooked through and grill marks show, about 3 minutes per side. (Alternatively, you can make patties through Step 3, cover and refrigerate; grill when ready to eat, adding 1 to 2 minutes per side if patties came out of refrigerator). Keep up to 5 days in the fridge or freeze for longer storage.