Stir together barbecue sauce and molasses. Set aside.
In a large bowl, mash beans. Stir in 3 tablespoons of the barbecue mixture (reserving remaining for brushing) and remaining ingredients — rice through egg white. Form into four 6 oz patties.
Heat olive oil in a cast iron or non-stick skillet over medium. Grill burgers for 2 minutes on one side. Turn and brush with remaining barbecue/molasses mixture. Top with Monterey Jack and grill for another 2 minutes or until cheese is melted.
Serve with lettuce, tomatoes, pickles, onions and mustard on a bun which has been grilled in butter.
Recipe adapted from www.food.com