In medium saucepot, cook bacon over medium-high heat 8 minutes or until almost crisp, stirring occasionally; drain all but 2 tablespoons drippings. Add onion; cook 4 minutes or until tender, stirring occasionally. Add garlic; cook 1 minute or until fragrant, stirring frequently. Stir in vinegar, sugar, coffee, thyme, allspice and red pepper; heat to a simmer. Reduce heat to low; simmer 10 minutes or until thickened and liquid is absorbed, stirring occasionally. Makes about 1 cup.
Prepare outdoor grill for direct grilling over medium-high heat. In large bowl, gently mix ground chuck and black pepper; do not overmix. Form ground chuck mixture into 4 (1/2-inch-thick) patties.
Spray patties with cooking spray; place on hot grill rack, cover and cook 6 minutes, turning once. Top patties with cheese; cover and cook 2 minutes or until internal temperature of burgers reaches 160° and cheese melts. During last minute of cooking, place buns, cut side down, on hot grill rack; cook 1 minute or until lightly toasted.
Heat large nonstick skillet over medium heat; spray with cooking spray. Add eggs; cover and cook 4 minutes or until egg whites are cooked through and yolks are slightly soft, or to desired doneness.
Spread bottom halves of buns with mayonnaise; serve burgers in buns topped with lettuce, bacon jam and eggs.