Add BBQ sauce and molasses to a small bowl. Stir to mix. Set aside.
Place beans into a large bowl. Mash beans to a paste.
Add 3 tablespoons BBQ mixture to beans (reserve remaining for brushing).
Add rice, oat bran, onions, beets, beet juice, chili powder, cumin, black pepper, salt, jalapeño and egg white. Mix well until completely combined.
Form mixture into four 6-ounce patties. Place on a plate and cover with plastic wrap. Place plate in refrigerator and chill for at least 2 hours or overnight.
When ready to serve, pour olive oil into a cast iron or nonstick skillet. Place over medium heat.
When oil is hot and shimmering, carefully add patties to pan. Grill burgers for 2 minutes on one side. Turn and brush with remaining barbecue and molasses mixture. Top with Monterey Jack cheese and grill for another 2 minutes or until cheese is melted.
Remove patties to a plate. Set aside and keep warm.
Toast hamburger buns, if desired.
Lay bun tops and bottoms, inside up, on serving plates.
Spread mustard on each bun top.
Layer lettuce, tomatoes, pickles and onions onto each bun top and place 1 pattie on each bun bottom. (See photo above)
Serve immediately, open faced.