Cook the pasta in a large pot of salted boiling water until al dente, about 8-10 minutes. Reserve some pasta water, then drain.

In a skillet, heat olive oil and sauté minced garlic until fragrant. Add broccoli, season with salt, and cook until tender, about 3-4 minutes.

In a saucepan, melt butter and whisk in flour to create a roux. Cook until smooth and lightly golden.

Gradually add milk while whisking. Cook until thickened, about 3-5 minutes. Stir in mustard powder, salt, black pepper, and paprika.

Reduce heat and stir in shredded cheese until melted and smooth.

Combine the drained pasta and broccoli with the cheese sauce, adding reserved pasta water to achieve desired consistency.

Serve warm, garnished with extra cheese or red pepper flakes as desired.