Bring about 4 quarts of salted water to a boil over high heat in a large pot. Add the pasta and cook according to package instructions until al dente, about 8 minutes. Drain and set aside.
Heat 1 ¼ cup of the milk in a medium saucepan over medium heat. Place the remaining ¼ cup of milk and cornstarch in a small bowl and whisk together until there are no lumps.
When the heated milk just begins to steam, whisk in the milk & cornstarch mixture. Continue whisking gently until the milk thickens slightly to coat the back of a spoon, about 3 to 4 minutes.
Turn the heat to low and add the shredded cheese, mustard powder, salt and Worcestershire. Stir until all the cheese has melted and the sauce is creamy. Add the broccoli and cook until the broccoli turns bright green (about 3 minutes).
Place the pasta into the pot with the broccoli and cheese sauce. Stir to coat the pasta evenly. Taste and adjust the seasonings as desired.