Prepare the Chicken: Season the chicken breasts with paprika, Italian seasoning, salt, and pepper. Set aside.
Cook the Potatoes: Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the potatoes and cook until golden and fork-tender, about 10 minutes. Remove and set aside.
Cook the Chicken: Add the remaining olive oil and butter to the skillet. Cook the chicken for 4-5 minutes per side or until golden brown. Remove and set aside.
Make the Sauce: Reduce heat to medium, then add garlic to the skillet and sauté for 1 minute. Stir in chicken broth, scraping up any browned bits. Add heavy cream and Parmesan cheese, stirring until smooth.
Combine and Finish: Return the chicken and potatoes to the skillet, spooning sauce over them. Cover and simmer for 5-7 minutes, or until the chicken is cooked through.
Serve: Garnish with fresh parsley and serve warm.