Cook the pasta according to the package instructions in a large pot of salted boiling water. Drain and set aside.
Season the diced chicken breasts with salt and pepper.
In a large skillet, cook the chopped bacon over medium heat until crispy. Remove the bacon from the skillet and place it on a plate lined with paper towels to drain excess grease. Leave about 1 tablespoon of bacon fat in the skillet.
In the same skillet with the bacon fat, add the seasoned chicken pieces. Cook until browned and cooked through, about 5-6 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the broccoli florets and minced garlic. Cook for 3-4 minutes, or until the broccoli is tender-crisp.
Pour in the heavy cream, shredded cheddar cheese, grated Parmesan cheese, dried thyme, and paprika. Stir well until the cheeses are melted and the sauce is smooth and creamy.
Add the cooked pasta, cooked chicken, and crispy bacon to the skillet. Stir until everything is evenly coated in the cheesy sauce. If the sauce is too thick, you can thin it out with a little pasta cooking water.
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