Bring 4 cups of salted water to a boil in a large pot. Add 12 oz of pasta and cook until al dente, about 9-11 minutes, then drain and reserve 1/2 cup pasta water.

In a skillet, heat 1 tsp of olive oil over medium heat. Add 1 minced clove of garlic and sauté until fragrant. Add 2 cups of broccoli florets and a pinch of salt. Cook until bright green, about 3-4 minutes.

In a saucepan, melt 2 tbsp of butter over medium heat. Whisk in 2 tbsp of flour to create a roux. Cook for about 1 minute. Gradually whisk in 2 cups of milk until the sauce thickens, about 4-5 minutes.

Reduce heat to low and stir in 1 cup of shredded cheddar cheese until melted. Mix in 1/2 tsp mustard powder, 1/2 tsp salt, 1/4 tsp black pepper, and 1/4 tsp paprika.

Add cooked pasta and sautéed broccoli to the cheese sauce. Toss to coat, adding reserved pasta water if needed to reach desired consistency.

Serve warm in bowls, garnished with additional cheese or red pepper flakes.