Bring a large pot of water to a boil and cook the pasta according to the package instructions, adding the broccoli about halfway through. When finished, drain the pasta and broccoli, reserving ½ cup of the cooking liquid, and set aside. Meanwhile, in a large skillet, brown the bacon until crisp, then remove to paper towels to drain, reserving the fat in the pan. Add 1 tablespoon of butter to the pan and cook the chicken until no longer pink in the middle, 7-8 minutes. Remove from the pan. Add the remaining butter to the pan along with the flour and garlic. Cook the flour for 30 seconds before whisking in the milks. Cook the sauce until it becomes thickened, then lower the heat and stir in the parmesan, salt and pepper. Return the pasta, chicken and bacon to the pan and stir everything to coat adding reserved liquid if the sauce needs thinning out. Serve immediately.