How to Make It
Preheat the oven to 400° and butter a shallow 9-by-13-inch ceramic baking dish.
Bring a large pot of salted water to a boil. Add the pasta and cook, following the package directions, until 4 minutes shy of al dente. Add the broccoli and cook an additional minute. Drain in a colander.
Warm the milk in the microwave or in a saucepan set over medium-low heat.
In a large pot or Dutch oven, melt the butter over medium-high heat. Whisk in the flour and cook until incorporated, 1 to 2 minutes. Add the warm milk and whisk gently over medium heat until the mixture has thickened enough to coat the back of a spoon, about 10 minutes.
Stir in the salt, pepper flakes, mustard and cheese. Add the pasta-broccoli mixture and toss to combine. Transfer to the prepared dish. Bake for 20 to 25 minutes, until tender and lightly browned.