In a large pot, bring about 4 quarts of water to a rolling boil and add a generous amount of salt. Cook your penne or rotini pasta until al dente, typically about 8-10 minutes. Once cooked, reserve 1/2 cup of pasta water before draining the pasta.

In a large skillet over medium heat, pour in 1 tablespoon of olive oil. Add minced garlic and sauté for approximately 30 seconds until fragrant. Toss in the broccoli florets, season with salt, and cook for around 3-4 minutes until slightly tender.

In a medium saucepan, melt 2 tablespoons of butter over medium heat. Whisk in 2 tablespoons of all-purpose flour, cooking it for about a minute. Gradually whisk in 2 cups of milk, ensuring no lumps. Cook until the sauce thickens, about 4-5 minutes; stir in mustard powder, salt, black pepper, and paprika.

Lower the heat and add 2 cups of shredded cheddar cheese to the cheese sauce, stirring until melted. Fold in the cooked pasta and sautéed broccoli, mixing until evenly coated. Add reserved pasta water to reach desired consistency.

Transfer to a serving bowl, garnish with additional shredded cheese or red pepper flakes, and serve warm.