01 -
In a large pot of boiling salted water, cook pasta according to package instructions; drain well.
02 -
Melt butter in a large cast iron skillet over medium high heat. Add garlic and shallot, and cook, stirring frequently, until fragrant, about 2 minutes.
03 -
Whisk in flour until lightly browned, about 1 minute. Gradually whisk in milk, half and half and Dijon mustard until slightly thickened, about 3-4 minutes. If the mixture is too thick, add more milk as needed; season with salt and pepper to taste.
04 -
Stir in pasta, broccoli, and cheese until well combined, about 3-4 minutes.
05 -
Serve immediately.