Melt 2 tablespoons of butter in a saucepan over medium heat. Whisk in 2 tablespoons of all-purpose flour and cook for 1-2 minutes until lightly golden. Gradually add 1 cup of whole milk, whisking constantly to avoid lumps, and continue cooking until thickened—about 3-5 minutes. Stir in 2 tablespoons of Dijon mustard, salt, and pepper to taste, then set aside to keep warm.

In a large mixing bowl, combine 1 cup of all-purpose flour, 2 teaspoons of baking powder, and a pinch of salt. Whisk together until well mixed. In another bowl, beat 2 eggs and mix in 1 cup of whole milk and 4 tablespoons of melted butter. Pour the wet ingredients into the dry ingredients, mixing gently until just combined.

Carefully fold in 1 cup of chopped shaved ham and 1 cup of grated Gruyere cheese into the waffle batter.

Heat your waffle maker on medium-high (around 375°F) and lightly grease it. Pour about ¾ cup of the waffle batter into the center of the preheated waffle iron and cook until golden brown and crisp, approximately 3-5 minutes.

Once the waffles are cooked, place them on a baking sheet. Top each waffle with the Dijon bechamel sauce, adding additional shaved ham and Gruyere cheese, then broil in the oven for 2-3 minutes until melted.

While broiling, prepare poached eggs by bringing water to a gentle simmer, adding a splash of vinegar, then poach for 4-5 minutes until the whites are set. Place one egg on each assembled waffle.