In a large pot, bring 4 cups of salted water to a boil over high heat.

Once boiling, add 12 ounces of pasta and cook according to package instructions until al dente, about 8-10 minutes. Drain and reserve ½ cup of the starchy water.

Heat 1 teaspoon of olive oil in a large skillet over medium heat, add 1 minced garlic clove and sauté for about 30 seconds.

Add 2 cups of broccoli florets to the skillet, sprinkle with salt and toss for 3-4 minutes until vibrant and slightly tender.

In a medium saucepan, melt 2 tablespoons of butter over medium heat and whisk in 2 tablespoons of flour, cooking until a smooth paste forms.

Gradually add 2 cups of milk while whisking until thickened, about 3-5 minutes.

Stir in mustard powder, salt, black pepper, and paprika. Reduce heat and add 1 cup of shredded cheddar cheese, stirring until melted.

Combine the drained pasta with the cheese sauce and fold in the sautéed broccoli. Adjust texture with reserved pasta water if necessary.

Serve warm, garnished with more cheese or red pepper flakes if desired.