Make the compote: Cook the bacon in a large skillet over medium heat, stirring occasionally, until crisp, about 4 minutes. Transfer to a paper towel-lined plate using a slotted spoon; discard all but 1 tablespoon of the drippings from the skillet.
Reduce the heat to low and add the butter to the skillet; swirl to melt. Add the onions; cover and cook, stirring occasionally, until golden, about 15 minutes. Uncover and add the garlic. Cook, stirring occasionally, until the onions are lightly caramelized, about 5 minutes. Add the vinegar and cook, stirring, until the onions are glazed, about 1 more minute. Stir in the reserved bacon and season with salt and pepper; set aside.
Grill the burgers: Preheat a grill to medium high and brush the grates with vegetable oil. Form the beef into four 1-inch-thick oblong patties and season with salt and pepper. Grill 4 to 5 minutes per side for medium. Meanwhile, toast the baguettes.
Serve the burgers on the baguettes; top with the gruyere, blue cheese, onion-bacon compote and arugula.
Photograph by Steve Giralt
Recipe courtesy of Father's Office for Food Network Magazine