Form the beef into four 6-ounce patties, about 3/4 inch thick; press the center of each patty with your thumb to make a 1/2-inch-deep indentation. Season the patties on both sides with salt and pepper. Lightly brush the grill grates with vegetable oil, then grill the patties, indentation-side up, until marked on the bottom, about 5 minutes. Flip and cook until marked and slightly firm, about 3 more minutes for medium doneness. Remove the patties to a plate and let rest 5 minutes. Grill the buns, cut-side down, until lightly toasted, about 1 minute.
Whisk the mustard, the remaining 1 tablespoon olive oil, the reserved 2 tablespoons bacon drippings and the shallot in a medium bowl. Season with salt and pepper. Add the frisee and toss; season with salt and pepper.
5. Spread the bun bottoms with mustard. Top with the burger patties, bacon, frisee salad and fried eggs. Cover with the bun tops.
Photograph by Levi Brown
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