Bring a large pot of salted water to a rolling boil over high heat. Add pasta and cook until al dente, about 8-10 minutes. Reserve 1/2 cup pasta water, drain, and set aside.

In a large skillet, heat olive oil over medium heat. Sauté minced garlic for about 30 seconds. Add broccoli florets, sprinkle with salt, and cook for 4-5 minutes until bright green.

In a medium saucepan, melt butter and whisk in flour to form a roux. Gradually add milk, whisking until thickened, about 3-5 minutes. Stir in mustard powder, black pepper, paprika, and cheese until melted.

Add the drained pasta into the cheese sauce, mixing gently to coat. Fold in sautéed broccoli and adjust consistency with reserved pasta water if needed.

Transfer to serving bowls, garnish with extra cheese or toppings, and serve warm.