In a medium saucepan, melt 2 tablespoons of butter over medium heat. Whisk in 2 tablespoons of flour, cooking for about 1-2 minutes until it turns a light golden color. Gradually add 1 cup of milk, stirring continuously until the mixture thickens into a creamy béchamel, approximately 5-7 minutes. Season with a pinch of nutmeg and salt, then set aside to keep warm.

Gather two slices of bread and spread a thin layer of butter on each side. On one slice, layer thinly sliced ham and a generous amount of grated gruyère cheese. Add the second buttered slice on top. Spread a thick layer of the prepared béchamel sauce over the top, adding more grated cheese to create a deliciously gooey layer for your Savory Croque Monsieur.

Heat a large skillet over medium heat. Carefully place the assembled sandwich in the skillet, cooking for about 3-5 minutes or until the bottom is golden brown and crispy. Gently flip the sandwich, pressing down slightly to ensure even cooking. Continue to cook the other side for another 3-5 minutes, monitoring closely to avoid burning.

For an extra touch of indulgence, transfer the sandwich to a baking sheet and place it under the broiler for 2-3 minutes. Keep a close watch as it broils, ensuring that the cheese melts and bubbles to a beautiful golden hue without burning.

Once perfectly cooked, remove the sandwich from the skillet or broiler and let it cool for a minute. Slice it in half to reveal the melty interior and serve hot.