Pulse the bacon and garlic in a food processor until coarsely ground.
Combine the ground pork, 1 teaspoon salt, 1/4 teaspoon pepper and the sage in a large bowl. Add the bacon mixture and gently mix with your hands. Gently form the meat into 4 balls, then lightly press into 4-inch-wide, 1-inch-thick patties. Make a 2-inch-wide indentation in the center of each with your thumb to prevent the burgers from bulging when grilled.
Preheat a grill to medium high. Season the patties with pepper. Grill, undisturbed, until marked on the bottom, 5 to 6 minutes. Turn and grill until the other side is marked and the patties feel firm, 4 to 6 more minutes. Meanwhile, spread the cut sides of the buns with butter and toast on the grill.