Preheat oven to 400°F (200°C).
Season chicken with salt, pepper, and paprika.
Heat olive oil and butter in an oven-safe skillet and sear chicken 3–4 minutes per side until golden, then remove.
Add potatoes and vegetables to the skillet and sauté 2–3 minutes.
Stir in garlic, chicken broth, heavy cream, and Boursin cheese until melted and smooth.
Return chicken to the skillet and spoon sauce over it.
Transfer skillet to oven and bake 18–22 minutes until chicken reaches 165°F (74°C).
Garnish with parsley and serve warm.