Bring a large pot of water to a rolling boil and cook pasta until al dente, about 8-9 minutes.
Meanwhile, heat olive oil in a large skillet over medium heat. Once hot, add minced garlic to the skillet and cook 30-60 seconds, or until fragrant, stirring constantly. Add half and half and milk; bring to soft boil. Add cheese and stir till it completely melts.
In a microwave-safe dish, microwave broccoli for 4-6 minutes or until al dente.
To the milk-cheese mixture, add cooked pasta and cook 1-2 minutes. Mix in the broccoli, bacon, and chicken and serve hot.