Adjust rack to upper position and preheat oven to 450 degrees. Bring a large pot of salted water to a boil. Heat a large pan over medium-high heat. Once hot, add bacon and cook, flipping occasionally, until crisp, 12-15 minutes. (TIP: Lower heat if bacon chars.) Transfer slices to a paper-towel-lined plate.

Pour bacon fat into a small heatproof bowl. Wipe out pan. Roughly chop bacon when cool enough to handle. Halve, peel, and thinly slice shallots. Once water boils, add cavatappi to pot. Cook, stirring occasionally, until al dente, 10-12 minutes. Carefully reserve 1 cup cooking water.

Wash and dry broccoli. Toss broccoli on a baking sheet with a drizzle of oil and a pinch of salt and pepper. Roast in oven until tender and edges are a little crisp, about 20 minutes. Meanwhile, pat chicken dry with a paper towel and season all over with salt and pepper.

Heat 1 tsp bacon fat in same pan over medium-high heat. Add chicken. Cook until no longer pink, 4-5 minutes per side. Transfer to a plate. Add a drizzle of oil and shallots to same pan over medium-high heat. Cook until softened, 2-3 minutes. Stir in demi-glace, 1/2 cup water, and 1 tsp sugar. Bring to a boil, then adjust heat to low. Cook, stirring, until thickened, 1-2 minutes. (TIP: Add a splash of water if very thick.) Remove from heat. Stir in 2 TBSP butter.

Heat 1 TBSP bacon fat in pot used for pasta over medium heat. Add flour and cook, stirring constantly, for 30 seconds. Slowly whisk in milk. Stir in a pinch of salt. Bring to a simmer and let thicken slightly, 1-2 minutes. Remove from heat and add Monterey Jack and cream cheeses, stirring until well combined. Stir cavatappi and 3/4 of the bacon into sauce in pot. Add a splash of reserved cooking water if very thick. Season with plenty of salt and pepper.

Divide chicken, broccoli, and mac ‘n’ cheese between plates. Spoon pan sauce over chicken. Sprinkle remaining bacon over mac ‘n’ cheese.