Preheat the Oven: Preheat the oven to 350°F/177°C so it is ready when the filled croissants are assembled.
Prepare the Croissants: Cut each croissant across about one-third from the top, then set the separated tops aside.
Shape the Filling Well: Slightly cut into the inside of each croissant and gently press the interior down to create a well for the filling.
Add the Mustard: Spread 1 teaspoon of Dijon mustard evenly into the well of each croissant.
Layer the Turkey: Place 2 slices of roasted turkey deli meat inside each croissant, arranging them over the mustard.
Add the Onions: Spoon 1 tablespoon of caramelized onions over the turkey in each croissant.
Add the Cheese: Place 1 slice of Havarti cheese over the caramelized onions.
Make Room for the Egg: Gently press down on the cheese to create a small nook that will hold the egg.
Add the Eggs: Crack 1 egg into the prepared nook of each croissant. Depending on the size of the eggs, remove some of the egg white if necessary to prevent it from overflowing. Arrange for Baking: Place each filled croissant onto a baking sheet, then repeat the preparation with the remaining croissants and ingredients.
Bake the Croissants: Bake at 350°F/177°C for 15 minutes, or until the egg is just set.
Finish and Serve: Remove the croissants from the oven and sprinkle the tops with ground pepper and chopped rosemary. Serve warm, either with the reserved croissant tops or without them.