In a very large skillet over medium-high heat, melt the butter and add the olive oil. Add the onions and cook, stirring often, until they soften and start to brown a bit, about 20 minutes. Add a bit more butter, oil or a splash of water or broth if they start to stick too much. Add the mushrooms to the pan and continue stirring another 10-15 minutes. Add the brown sugar and the balsamic vinegar. Stir it in well, and continue to cook until the onions are nicely browned and softened. Remove from heat and season with salt and pepper to taste.
In a large bowl, combine ground beef, Dijon, paprika, salt, pepper and the eggs. Using your hands, mix all the ingredients well and form into 8 patties.
Heat a grill to medium-high. Cook the burgers on each side until nicely browned, 6-8 minutes on each side, depending on thickness. Brush generously with BIG DIPPER BBQ SAUCE and flip one more time to heat and caramelize the sauce. Burgers should read 160°F internal temperature.
Dress buns with more BIG DIPPER BBQ SAUCE, and top with burgers, onions and mushrooms and whatever other toppings you like. Serve with fries and extra BIG DIPPER BBQ SAUCE for dipping.
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