1. For the topping: Process the bread and butter in a food processor until coarsely ground, about six 1-second pulses; set aside.
2. For the filling: Adjust an oven rack to the middle position and heat the oven to 400 degrees. Bring 4 quarts of water to a boil in a large pot. Add 1 tablespoon salt and the broccoli to the boiling water; cover and cook until bright green and crisp-tender, about 3 minutes. Drain the broccoli and leave it in the colander; set aside.
3. Meanwhile, melt the butter in a medium saucepan over medium heat. Stir in the garlic, mustard, and cayenne; cook until fragrant, about 30 seconds. Add the flour and cook, stirring constantly, until the flour turns golden, about 1 minute. Slowly whisk in the broth and milk; bring to a simmer and cook, whisking often, until large bubbles erupt at the surface and the mixture is slightly thickened, about 5 minutes. Off the heat, whisk in the colby and cheddar. Season to taste with salt and pepper.
4. Spread the broccoli in a 13 by 9-inch baking dish (or shallow casserole dish of similar size). Whisk the cheese sauce again briefly and pour over the broccoli. Sprinkle with the bread-crumb topping. Bake until golden brown and bubbling around the edges, about 15 minutes. Cool for 5 minutes before serving.
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