Pat the chicken breasts dry and season both sides with salt and pepper. Lightly dredge each piece in flour, shaking off the excess.
Heat olive oil and butter in a large skillet over medium heat. Once hot, add the chicken and cook until golden brown on both sides, about 4–5 minutes per side. Remove the chicken from the skillet and set aside.
In the same skillet, add minced garlic and cook for about 30 seconds until fragrant. Stir in Dijon mustard and chopped rosemary, letting the flavors bloom.
Pour in the white wine, scraping up any browned bits from the bottom of the pan. Let it simmer for 2–3 minutes to reduce slightly.
Reduce heat to low and stir in the heavy cream. Let the sauce simmer gently for 3–4 minutes until it thickens slightly.
Return the chicken to the skillet and spoon the sauce over each piece. Simmer for an additional 5 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
Taste and adjust seasoning with salt and pepper as needed. Serve immediately over pasta, potatoes, or alongside warm sourdough bread for a cozy, comforting meal.