Bring a large pot of salted water to a boil and cook bowtie pasta according to package directions until al dente. Drain and set aside.
In a mixing bowl, toss the cubed chicken with the Cajun seasoning until all pieces are uniformly coated.
Heat olive oil in a large skillet over medium-high heat. Add the chicken and sauté for 5 to 7 minutes or until the internal temperature reaches 165 degrees Fahrenheit (74 degrees Celsius). Remove chicken from the skillet and set aside.
In the same skillet over medium heat, melt the butter. Add the minced garlic and sauté for 60 seconds until fragrant.
Pour in the heavy cream and bring to a gentle simmer, whisking constantly to incorporate any browned bits from the chicken.
Reduce heat to low and gradually whisk in the Parmesan cheese and mozzarella cheese until the sauce is smooth and thickened.
Season the sauce with salt and black pepper.
Incorporate the cooked pasta and sautéed chicken back into the skillet, tossing thoroughly to ensure even distribution of the Alfredo sauce.
Garnish with chopped parsley and serve immediately.