Cook bacon, stirring occasionally, in a large nonstick skillet over medium-high heat until brown and crisp, 10–12 minutes. Transfer to paper towels. Reserve 3 Tbsp. bacon fat; wipe skillet clean.

Whisk vinegar, mustard, honey, and ½ tsp. salt in a small bowl, then gradually whisk in reserved bacon fat. Keep warm.

Generously butter cut sides of each bun. Toast buns, cut side down, in same skillet over medium-high heat, pressing gently to make contact with skillet, until golden brown, about 2 minutes. Transfer to a plate.

Wipe skillet clean. Heat 1 Tbsp. butter over medium-high until foaming. Crack eggs into skillet; reduce heat to medium-low. Cook, undisturbed, until whites are set but yolks are still runny, about 3 minutes; season with salt and pepper.

Toss frisée or other leafy green, Gorgonzola, bacon, and vinaigrette in a medium bowl to combine. Pile salad on bottom half of buns, dividing evenly, and top each with an egg. Close up sandwiches.