Step 1

Combine mayonnaise; chipotle; Worcestershire; maple syrup, if using; and ½ teaspoon pepper in bowl. Set aside.

Step 2

Combine ground beef and sausage in large bowl and knead with your hands until roughly combined. Divide meat mixture into 4 equal portions, then shape each portion into 4½-inch-wide patty. Using your fingertips, press center of each patty to create slight divot. (Patties can be covered with plastic wrap and refrigerated for up to 24 hours.)

Step 3

Cook bacon in 12-inch nonstick skillet over medium heat, flipping occasionally, until crispy, 8 to 10 minutes. Transfer bacon to paper towel–lined plate. Pour off and reserve all but 1 teaspoon fat from skillet.

Step 4

Heat fat left in skillet over medium-high heat until just smoking. Sprinkle patties with ¼ teaspoon salt and remaining ¼ teaspoon pepper. Transfer patties to skillet and cook until well browned on first side, 4 to 6 minutes. Flip patties, top with cheddar, and reduce heat to medium-low. Continue to cook until browned on second side and meat registers 160 degrees, 5 to 7 minutes longer.

Step 5

Transfer burgers to second paper towel–lined plate. Pour off fat from skillet. Wipe skillet clean with paper towels.

Step 6

Crack eggs into 2 small bowls (2 eggs per bowl) and sprinkle with remaining pinch salt. Add 1 tablespoon reserved bacon fat to now-empty skillet and heat over medium-high heat until shimmering. Swirl to coat skillet with fat, then, working quickly, pour 1 bowl of eggs in 1 side of skillet and second bowl of eggs in other side. Cover and cook for 1 minute. Remove skillet from heat and let sit, covered, for 15 to 45 seconds for runny yolks (white around edge of yolk will be barely opaque), 45 to 60 seconds for soft but set yolks, or about 2 minutes for medium-set yolks.

Step 7

Spread mayonnaise mixture on cut sides of buns. Place burgers on bun bottoms, then top with bacon, eggs, and bun tops. Serve.