How to Make It
Preheat the oven to 325°F. Line a rimmed baking sheet with aluminum foil and fit with a wire rack. Put the dulce de leche and cayenne pepper in a bowl and mix well. Add the bacon and toss gently with your hands until evenly coated. Place the bacon in a single layer on the wire rack and put sprigs of rosemary on top. Refrigerate for 10 minutes to set.
Bake the bacon until slightly dark (not burnt) and crispy, about 45 to 55 minutes total, rotating the pan halfway through baking and removing the end pieces and the rosemary after about 40 minutes if they are browning quickly. Let cool for 15 minutes.
While the bacon is cooling, bring a small pan of salted water to a boil. Carefully lower the eggs into the boiling water with a slotted spoon and boil for 5 minutes. Drain the eggs, cut off the lids and serve with a pinch of salt and pepper in egg cups for individual servings or in an egg carton if serving family style. Serve the bacon soldiers alongside for dipping into the eggs.