Boil pasta according to directions listed on package adding broccoli during last 3 - 4 minutes of boiling, drain well (reserve 1/4 cup pasta water, just in case you want to thin pasta sauce).
Meanwhile, in a pot melt butter over medium heat then stir in flour. Cook mixture stirring constantly for 1 minute.
While whisking vigorously, slowly add in milk, then season with onion powder, garlic powder and salt and pepper to taste. Increase heat to medium-high, cook mixture, stirring constantly until it boils and thickens.
Remove from heat, allow to cool for 1 minute then add in cheddar and parmesan cheese and stir until melted. Add drained pasta and broccoli and chicken and toss to evenly coat. As it sits it will thicken, you can thin it with a few tbsp pasta water if desired.
*I think fresh broccoli is best in this shells and cheese recipe, but if you use frozen I recommend thawing it first and draining it before adding it to the boiling pasta water.
**If you want a stronger cheddar cheese flavor, use 8 oz. You can also use extra sharp cheddar.