A golden Croque Madame topped with a perfectly fried egg elevates ham, cheese, and béchamel into a protein-packed brunch indulgence. This French-inspired American bistro favorite is rich, satisfying, and family-worthy.
Preheat oven to 400°F. Line a baking sheet with parchment paper.
Prepare béchamel: In a saucepan over medium heat, melt 2 tbsp butter, whisk in flour, and cook for 1 minute. Slowly add milk, whisking continuously, until thickened. Season with salt, pepper, and nutmeg. Remove from heat.
Lay out 4 slices of bread. Spread a generous layer of béchamel on each, then top with ham and half the cheese. Cover with remaining bread slices and spread more béchamel and cheese on top.
Transfer sandwiches to baking sheet; bake for 10–12 minutes until cheese melts and edges turn golden.
Meanwhile, heat remaining butter in a skillet over medium-high. Fry eggs until whites are set and yolks are just runny. Top each sandwich with a fried egg and serve immediately.