Step 1

To prepare cheese sauce: Melt butter in a medium saucepan over medium heat. Add flour and whisk constantly until thickened and just starting to turn light brown, 2 to 3 minutes. Slowly add milk, whisking constantly. Cook, stirring often, until the mixture is thick enough to coat the back of a spoon, 10 to 12 minutes. (Do not boil.) Remove from heat and, a handful at a time, whisk in Cheddar and Parmesan until smooth. Stir in 1/2 teaspoon salt. (Reserve 1 1/2 cups for another use.)

Step 2

Meanwhile, prepare pasta & vegetables: Bring a large pot of water to a boil. Add pasta and cook for 4 minutes less than package directions. Stir in Brussels sprouts and cauliflower and continue cooking until the pasta and vegetables are tender, 4 to 5 minutes more. Drain well.

Step 3

Dry the pot and set over medium heat. Add oil and garlic and cook until the garlic is fragrant and just starting to brown, about 1 minute. Add the hot pasta and vegetables and stir to combine. Add 2 1/2 cups of the cheese sauce and salt; reduce heat to medium-low and stir until steaming-hot, about 1 minute. (Do not boil.)