Pat chicken dry. Season both sides with salt and pepper, then lightly coat with flour.
Heat a Dutch Oven over medium heat. Add butter and olive oil to the skillet. Add chicken, and cook 3-4 minutes per side, until golden brown. Remove chicken and set aside.
Add potatoes to the Dutch oven and sauté for 5 minutes. Remove potatoes and set aside.
Add garlic, chicken stock, and heavy cream to the skillet. Stir and bring to a simmer.
Add chicken and potatoes to the Dutch oven. Bake, covered, for 15 minutes, then uncover and bake for another 15 minutes, until the internal temperature of the chicken reaches 165F and the sauce is thickened.
Serve with grated parmesan cheese and fresh basil.
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