Bring a large pot of salted water to a boil and cook the shell pasta according to package directions; add the diced broccoli during the last 3–4 minutes of cooking. Drain well, reserving 1/4 cup pasta cooking water in case you need to thin the sauce.
Meanwhile, melt the butter in a saucepan over medium heat. Sprinkle in the flour and cook, stirring constantly, for 1 minute to make a roux.
Whisking constantly, slowly pour in the milk. Add the onion powder, garlic powder, and salt and pepper to taste. Increase heat to medium-high and cook, stirring, until the sauce comes to a boil and thickens.
Remove the sauce from heat and stir in the shredded cheddar and grated Parmesan until fully melted and smooth.
Add the drained pasta, broccoli, and shredded chicken to the cheese sauce; toss gently to coat evenly. If the sauce becomes too thick, thin with a few tablespoons of the reserved pasta water.
Serve immediately while hot.
