Bring a large saucepan of water to a boil. Cook noodles for 4 minutes.
Add frozen broccoli and continue cooking, stirring occasionally, until the pasta and broccoli are just tender, 4 to 5 minutes more.
Meanwhile, heat ¾ cup milk in another large saucepan over medium-high heat until just simmering.
Whisk the remaining ¼ cup milk, flour, garlic powder, salt and pepper in a small bowl until combined.
Add the flour mixture to the simmering milk.
Return to a simmer and cook, whisking constantly, until the mixture is thickened, 2 to 3 minutes.
Remove from the heat and whisk in cheddar, Parmesan and mustard until the cheeses are melted.
Drain the pasta and broccoli and add to the cheese sauce.
Return to the heat and cook, stirring, over medium-low, until heated through, about 1 minute.