To prepare topping: In a food processer, combine bread and butter and pulse until coarsely ground, about six 1-second pulses; set aside.
To prepare filling: Preheat oven to 400 degrees. Bring 4 quarts of water to boil in a large pot. Add 1 tablespoon salt and broccoli to boiling water, cover and cook until broccoli is bright green and crisp-tender, about 3 minutes. Drain broccoli and leave in colander; set aside.
Meanwhile, melt butter in a medium saucepan over medium heat. Stir in garlic, mustard and cayenne; cook until fragrant, about 30 seconds. Add flour and cook, stirring occasionally, until flour turns golden, about 1 minute. Slowly whisk in milk and broth. Bring to a simmer and cook, whisking often, until large bubbles erupt at the surface and mixture is slightly thickened, about 5 minutes. Remove from heat, whisk in Colby and Cheddar cheeses. Season to taste with salt and pepper.
Spread broccoli in a 9x13-inch baking pan (or shallow casserole dish of a similar size). Whisk cheese sauce again briefly and pour over broccoli. Sprinkle with bread-crumb topping. Bake until golden brown and bubbling around the edges, about 15 minutes. Remove from oven, cool for 5 minutes and serve.