In small saucepan, melt 3 tablespoons butter over medium-high heat. Add flour and whisk continuously until bubbly and light brown, 4 to 5 minutes.
Add milk, whisking continuously, and bring to a boil, then reduce heat to low and let simmer until thickened, whisking regularly, 5 minutes more.
Add half the Gruyere, whisking until smooth, then whisk in a pinch of nutmeg and season with salt and pepper. Let cool slightly.
Heat broiler. Arrange slices of bread on a baking sheet. Spread ½ tablespoon Dijon on each slice and layer with ham and tomato.
Cover with about 2 tablespoons cheese sauce and about 3 tablespoons shredded cheese. Toast under broiler for 1½ to 2 minutes (watch carefully so it doesn’t burn!) until cheese melts.
In a large nonstick skillet, heat remaining 2 tablespoons butter over medium-high heat, then add eggs and reduce heat to medium.
Cook eggs, basting regularly with butter, until whites are set and yolks are still slightly runny, about 4 minutes. Season with salt and pepper, and top each sandwich with an egg.
In large bowl, whisk together remaining 1 teaspoon Dijon, red wine vinegar, and olive oil, and season with salt and pepper. Add greens and dill, tossing gently to combine. Serve with sandwiches.
- Five tablespoons of unsalted butter
- Three tablespoons flour
- Five oz of Gruyere, divided
- Pinch of nutmag
- Kosher salt
- Frashly ground peper
- 4 slices of whole wheat bread
- 2 tablespoons plus one tsp of dijon mustard
- 1/3lb of ham
- 2 tomatos, cut thin
- 4 large eggs
- 6 c. Salad greens
- 1/4 c. Freash dill