Cut broccoli into bite-sized pieces.
Pat chicken dry, and season both sides with ¼ tsp. salt and a pinch of pepper.
Add pasta to boiling water and cook until al dente, 8-9 minutes.
Reserve ¾ cup pasta water, then drain pasta in a colander.
While pasta cooks, roast broccoli.
Roast the Broccoli
Toss broccoli with 1 tsp. olive oil, ¼ tsp. salt, and a pinch of pepper on prepared baking sheet.
Spread into a single layer. Roast until lightly browned, 11-13 minutes.
Transfer broccoli to a plate. Broccoli will finish cooking in a later step.
Replace foil on baking sheet.
While broccoli roasts, cook chicken.
Cook the Chicken
Heat 1 tsp. olive oil in a medium non-stick pan over medium-high heat.
Add chicken to hot pan. Cook until lightly browned and chicken reaches a minimum internal temperature of 165 degrees, 4-5 minutes per side.
Transfer chicken to a mixing bowl and cover. Rest at least 5 minutes.
Once chicken cools, shred into bite-sized pieces and season with BBQ seasoning.
Reserve pan; no need to wipe clean.
While chicken rests, make sauce.
Make the Sauce
Return pan used to cook chicken to medium-high heat.
Add ½ tsp. olive oil and garlic to hot pan. Stir occasionally until aromatic, 30-60 seconds.
Add reserved pasta water and cream and bring to a simmer. Cook until thick enough to coat the back of a spoon, 2-4 minutes.
Remove from burner and stir in half the cheese (reserve remaining for topping pasta).
Bake the Pasta
Stir chicken, broccoli, and pasta into sauce. Transfer to prepared casserole dish and top with remaining cheese.
Place casserole dish on prepared baking sheet to catch any drips. Bake until cheese is melted, 4-6 minutes.
Plate dish as pictured on front of card. Bon appétit!