Bring a large pot of salted water to a boil. Cook the bowtie pasta until al dente according to the package instructions, then drain and set aside.
Heat 2 tablespoons of butter and the olive oil in a deep skillet over medium-high heat. Add the chicken and season with Cajun seasoning, garlic powder, onion powder, Italian seasoning, and black pepper. Cook for 5–7 minutes, until golden and cooked through. Transfer the chicken to a plate.
Reduce the heat to medium and melt the remaining 2 tablespoons of butter in the same skillet. Add the minced garlic and sauté until fragrant.
Pour in the chicken broth and heavy cream. Add the Velveeta, cream cheese, and mozzarella, stirring gently until the cheeses melt and the sauce becomes smooth and creamy.
Return the cooked chicken to the skillet and add the drained pasta. Toss until everything is evenly coated in the garlic butter sauce.
Stir in the Parmesan cheese until melted. Taste and adjust the salt as needed.
Serve immediately while warm and creamy.