Step 1Heat a skillet over medium-high heat. Fry the bacon until crisp, 5 to 6 minutes, then remove to paper towels to drain. Crumble 1 of the slices and set aside; reserve the rest of the bacon for another use. Measure 2 tablespoons of the bacon fat into a medium heavy skillet.
Step 2Add the onions to the skillet and sprinkle with the sugar. Cook until the onions are golden brown, about 20 minutes. Halfway through, stir in the crumbled bacon. At the end of the 20 minutes, stir in the balsamic vinegar, ketchup, Worcestershire sauce, liquid smoke, salt and pepper. Cook for 2 more minutes. Set aside.
Step 1Combine the strip and rib-eye steaks and mix in the salt. Shape the meat into 4 (7-inch) oval patties, about 3/4 inch thick.
Step 2Melt 1 tablespoon of butter in a large skillet, preferably cast-iron, over medium-high heat. Fry the burgers, 2 at a time, for 3 minutes, then flip. Top each burger with 1/4 of the blue and Gruyere cheeses. Cook the burgers 3 more minutes for medium.
Step 3Remove and keep warm; melt the remaining butter in the skillet and repeat with the remaining 2 patties and cheeses.
Step 4To assemble, place the burgers on the baguettes and top with the onions and arugula, dividing evenly.