Toss together Monterey Jack and sharp cheddar in a large bowl with your hands. Sprinkle cornstarch over and toss again until cheese is evenly coated. Set cheese mixture aside.
Bring water to a boil in a large Dutch oven or other heavy pot. Add pasta and cook until very al dente.
Add frozen broccoli florets and whole milk to pot and return to a boil. Cook until pasta and broccoli are both tender but not mushy.
Reduce heat to low and mix in English mustard powder, salt, and pepper. Add reserved cheese mixture a handful at a time, stirring after each addition.
Remove pot from heat. Taste broccoli mac and cheese and season with more salt and pepper if needed. Let sit until cheese sauce has thickened slightly before serving.
