Step 1Heat the oven to 400 degrees.
Step 2Roast the shallots with the butter and salt and pepper to taste in a small ovenproof skillet until golden, about 25 minutes. Shake the skillet frequently. Remove from the oven and place the skillet on the stove top over medium heat. Add the honey and balsamic vinegar and cook until reduced to a syrupy consistency, 6 to 8 minutes. (Makes 1/4 cup.)
Step 1Heat a skillet over medium-high heat. Fry the bacon until crisp, 5 to 6 minutes, then remove to paper towels to drain. Set aside.
Step 2Combine the strip and rib-eye steaks and mix in the salt. Shape the meat into 4 (4 1/2-inch) patties.
Step 3Melt 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. Add 2 slices of the Brie to each patty and cook 3 more minutes for medium. Remove and keep warm; melt the remaining butter in the skillet and repeat with the remaining 2 patties. (You can grill the patties, if you prefer.)
Step 4To assemble, place the burgers on the buns. Top them with the bacon slices and Balsamic shallot marmalade, dividing evenly.