Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil. Cook the bowtie pasta until just al dente according to the package directions. Drain and set aside.
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the chicken and season with paprika, salt, black pepper, Italian seasoning, thyme, and basil.
Cook the chicken for 5–7 minutes, stirring occasionally, until golden and cooked through. Transfer it to a plate and set aside.
Reduce the heat to medium. Add the remaining 3 tablespoons of butter to the same skillet. Once melted, add the garlic and cook for about 30 seconds, just until fragrant.
Sprinkle in the flour and whisk continuously for about 1 minute to remove the raw flour taste.
Slowly pour in the chicken broth and heavy cream while whisking to create a smooth sauce. Simmer gently for 3–4 minutes until slightly thickened.
Reduce the heat to low and stir in the Parmesan cheese and ½ cup of mozzarella. Continue stirring until the cheese has melted and the sauce is smooth.
Add the cooked bowtie pasta, chicken, and fresh parsley to the skillet. Toss until everything is evenly coated in the creamy herb sauce.
Transfer the mixture to the prepared baking dish and spread it into an even layer. Sprinkle the remaining 1 cup of mozzarella evenly over the top.
Bake uncovered for 18–22 minutes, or until the sauce is bubbling around the edges and the cheese is fully melted.
For a more golden topping, broil for 1–2 minutes while watching carefully to prevent burning.
Remove from the oven and allow the pasta bake to rest for 5 minutes before garnishing with additional parsley and serving.