Prepare the potatoes first. Wash and halve baby potatoes into evenly sized pieces so they cook at the same rate. Pat them completely dry with paper towels to help them brown properly in the skillet.
Heat olive oil in a large skillet over medium heat. Add the potatoes cut side down in a single layer. Season lightly with salt and pepper. Cook for 10 to 12 minutes, turning occasionally, until golden brown and beginning to soften. Remove from skillet and set aside.
While potatoes cook, pat chicken breasts dry and season both sides evenly with salt, pepper, paprika, and Italian seasoning. If breasts are thick, pound lightly to ensure even cooking.
In the same skillet, melt butter over medium heat. Add the chicken in a single layer and sear for 4 to 5 minutes per side until golden brown. The chicken does not need to be fully cooked yet. Remove and set aside.
Lower heat to medium-low and add minced garlic to the skillet. Sauté for about 60 seconds until fragrant, stirring constantly to prevent burning.
Pour in the chicken broth to deglaze the skillet. Use a wooden spoon to scrape up browned bits from the bottom of the pan. Allow the broth to simmer for 2 to 3 minutes so flavors concentrate.
Stir in heavy cream and Parmesan cheese. Simmer gently for 3 to 5 minutes until the sauce begins to thicken slightly. Avoid boiling, which may cause separation.
Return the potatoes to the skillet and nestle the chicken on top. Spoon some sauce over the chicken to coat. Cover the skillet with a lid and reduce heat to low.
Simmer for 10 to 15 minutes, or until chicken reaches an internal temperature of 165°F and potatoes are fork tender. If sauce becomes too thick, add a splash of broth to loosen.
Taste and adjust seasoning if needed. Garnish with chopped parsley and serve directly from the skillet while warm.