1. Bring a large pot of water to a boil. Cook pasta for 4 minutes. Add frozen broccoli and continue cooking, stirring occasionally, until the pasta and broccoli are just tender, 4 to 5 minutes more.
2. Meanwhile, heat 1 1/2 cups milk in another large pot over medium-high heat until just simmering. Whisk the remaining 1/4 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.
3. Remove from the heat and whisk in Cheddar, Parmesan and mustard until the cheese is melted.
4. Drain the pasta and broccoli and add to the cheese sauce. Add in the spinach. Return to the heat and cook, stirring, over medium-low heat, until heated through, and spinach is wilted.
5. Sprinkle pepper on top when serving (to taste).