Wipe the grate of your grill or your skillet with olive oil before heating over a medium-high flame.
Cook the bacon in a dry skillet over medium heat; when done to your like, place on paper towels to drain and set aside.
In a medium bowl, combine the ground beef, salt, pepper, thyme and sage; mix well using your hands and form into 8 thin patties; form small craters in the center of half of the patties, leaving an edge of about a quarter inch all the way around and place a scant 2 tablespoons of blue cheese in the center; top each with another patty, pinching the seams together, making sure the stuffing is completely covered.
Cook the burgers over medium-high heat until medium-rare; 4 minutes per side on the grill and 4 1/2 minutes per side in a skillet; be gentle when turning the patties so they don't split.
Thinly slice the apple and top each burger with the slices just before removing from the heat.
Serve the burgers topped with bacon on the toasted roll.