Preheat the oven to 350 degrees F.

Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until just slightly softened, about 6 minutes. Reserve 1 cup of pasta cooking water, then drain the pasta and rinse under cold water.

Meanwhile, remove the crusts from the bread and cut into 1-inch cubes. Pulse in the food processor until the bread breaks into bean-sized pieces.

Melt 3 tablespoons of the butter in a large skillet over medium heat. Add the breadcrumbs and cook, stirring, until toasted, 5 to 10 minutes. Remove from the heat and season with salt and pepper.

Melt 4 tablespoons of the butter in a large saucepan over medium heat. Whisk in the flour, mustard powder, and cayenne. Cook, whisking constantly, until smooth and slightly golden, about 2 minutes. Whisk in the milk and cook, whisking occasionally, until the sauce begins to boil and thicken, about 7 minutes, then remove from heat. Stir in the fontina, Gruyere, and all but 1 1/2 cups of the Cheddar until fully melted. Stir in the pasta, adding the reserved pasta water as needed to make a creamy sauce. Season with salt and pepper.

Melt the remaining 1 tablespoon butter in a small bowl in the microwave. Brush a 9-by-13-inch glass or ceramic baking dish with the melted butter. Spread the pasta mixture in the prepared dish. Sprinkle the remaining Cheddar evenly over the pasta, then scatter the toasted breadcrumbs on top. Bake until heated through and just bubbling, about 25 minutes. Let rest for 10 minutes before serving.