Cook the pasta in salted boiling water until al dente. During the last 3 minutes, toss in the broccoli florets. Drain and set aside.
In a large skillet, melt the butter over medium heat. Whisk in the flour to make a roux and cook for about 1 minute.
Slowly pour in the milk and vegetable broth, whisking constantly to avoid lumps. Cook until the sauce thickens, about 5 minutes.
Stir in the cheddar cheese and garlic powder until smooth and creamy.
Add the cooked pasta and broccoli to the skillet, tossing everything together until coated in the cheesy sauce.
Taste and season with salt, pepper, and red pepper flakes if you want a bit of heat. Serve hot.