To prepare the onion marmalade, heat 1 tablespoon olive oil in a large skillet over medium high. Add onions, brown sugar, and salt. Sauté for 15 minutes, stirring occasionally, until dark golden brown and tender. Add balsamic vinegar and cook 2 additional minutes. Set aside.
Meanwhile, heat a large oven proof skillet over medium high. Place rack in the upper third of your oven and set oven broiler to high.
Next, prepare the burger patties by mashing the black beans in a large bowl. Add beaten egg, 3 tablespoons extra virgin olive oil, 1 tablespoon Dijon mustard, garlic powder, salt, pepper, and worcestershire. Mix until incorporated.
Add beef and stir in gently with a fork, being careful not to compress the meat. Divide the mixture into 6 portions and shape into approximately 3 1/2 inch-wide patties. Brush each side of the patties with remaining mustard.
Brush the skillet with extra virgin olive oil to prevent sticking. Add the burgers to the skillet and cook for 3-4 minutes, until the mustard forms a golden crust. Flip, top with blue cheese, then cook for 3 additional minutes, longer if you prefer the burgers more well done.
During the last moments of cooking, place the skillet under the oven broiler for 30 seconds to finish melting the blue cheese.
Top blue cheese burgers with a heaping spoonful of onion marmalade and serve immediately on toasted buns.
Notes
TO STORE: Keep leftover burgers, deconstructed, in an airtight container for up to 3 days in the fridge. Onion marmalade may be kept in a separate airtight container in the fridge for up to 5 days.
TO REHEAT: Gently warm marmalade in the microwave until heated through. Reheat the burgers in a nonstick skillet with a bit of water, covered to help them steam and not dry out. Top with blue cheese, broil to melt and then serve topped with marmalade on buns.
TO FREEZE: Cooked burger patties may be kept frozen for up to 3 months in a freezer-safe container. Let thaw overnight in the refrigerator prior to reheating.