Sunny-side-up eggs shine atop this cheesy casserole inspired by the classic French sandwich. We used turkey pastrami, but you can of course go traditional and sub in ham.
Preheat oven to 450 degrees. Trim ends of bread so it fits in a 9-by-13-inch baking dish, then toast directly on oven rack until crisp, 8 to 10 minutes. Melt 3 tablespoons butter in a saucepan over medium-high heat. Add flour; cook, whisking, until golden, 2 minutes. Whisk in milk. Boil, still whisking, until thickened, 2 minutes. Remove from heat. Whisk in Dijon, 1 cup cheese, 1 teaspoon salt, and 1/4 teaspoon pepper. Spread 3/4 cup cheese sauce evenly in bottom of dish. Nestle bread into sauce, cut-side up. Top with pastrami and remaining cheese sauce. Sprinkle with remaining 3/4 cup cheese.
Bake until bubbly and browned in places, 15 to 18 minutes. Fry eggs in remaining 1 tablespoon butter in a large nonstick skillet over medium-high heat until whites are set but yolks are still runny, 2 to 3 minutes. Top toasts with eggs; sprinkle with chives and serve.