Cook the penne pasta: Bring a large pot of salted water to a boil. Cook the penne pasta according to package instructions until al dente. Reserve 1 cup of pasta water before draining.
Cook the chicken: In a large skillet, heat the olive oil over medium-high heat. Add the chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside
Soften the onion and garlic: In the same skillet, add the diced onion and cook until softened, about 3-4 minutes. Add the minced garlic and cook for an additional minute.
Add the chicken broth and heavy cream: Pour in the chicken broth and heavy cream, and bring the mixture to a simmer. Let cook for 2-3 minutes, until slightly thickened.
Add the cheese and thyme: Stir in the shredded cheddar cheese and grated Parmesan cheese until melted and smooth. Add the dried thyme and paprika, and season with salt and pepper to taste.
Combine the chicken and pasta: Add the cooked chicken back into the skillet, and stir to combine with the cheese sauce. Add the cooked penne pasta to the skillet, and toss to combine with the chicken and cheese sauce. If the sauce seems too thick, add some of the reserved pasta water.
Serve: Serve the Crack Chicken Penne hot, garnished with chopped fresh parsley.