In a medium saucepan, melt the butter over medium heat, stir frequently. Whisk in flour until bubbling, about 2 minutes. Gradually add milk, whisking continuously until thick, about 5 minutes. Stir in Dijon mustard and season with salt and pepper.

In a large mixing bowl, combine flour, baking powder, and salt. In another bowl, whisk together eggs, milk, and melted butter. Pour wet ingredients into dry, mix gently. Fold in ham and cheese, careful not to overmix.

Preheat your waffle maker and lightly grease. Pour 3/4 cup of the batter into the hot maker. Cook until golden brown and crispy, about 4-5 minutes. Carefully remove the waffles.

On a baking tray, place each waffle and top with béchamel sauce, sprinkle with additional ham and cheese. Broil for 2-3 minutes, watching closely until cheese is bubbly.

While waffles are broiling, poach or fry the eggs. Once waffles are ready, transfer to plates. Top with poached or fried eggs and add chives for garnish.