In a small bowl, whisk together the Dijon mustard, minced garlic, 1 tbsp olive oil, and a pinch of black pepper until smooth. Place the chicken breast halves in a shallow dish or resealable bag, pour the marinade over them, and refrigerate for at least 30 minutes.

Preheat your oven to 375 degrees F. Remove chicken from the fridge and let it rest at room temperature for 10 minutes. Lightly coat each piece in all-purpose flour and season with salt and pepper.

Heat olive oil and butter in an oven-safe skillet over medium-high heat. Once the butter is foaming, sear the chicken for 3 minutes per side until deep golden brown. Do not move the chicken while searing. Work in batches if needed to avoid crowding the pan.

Remove the chicken and set aside. Add the garlic and rosemary sprigs to the hot skillet. Stir for 30 seconds until fragrant, then pour in the white wine to deglaze, scraping up the browned bits from the bottom of the pan.

Whisk in the Dijon mustard and heavy cream. Stir over medium heat until smooth and slightly thickened, about 2 to 3 minutes. Taste and adjust seasoning. If sauce is too thick, add a splash of white wine.

Return the seared chicken to the skillet, nestling it into the sauce. Transfer the skillet to the oven and bake uncovered for 25 to 30 minutes, basting with pan juices halfway through.

Use a meat thermometer to confirm the internal temperature reaches 165 degrees F. Remove from the oven and let the chicken rest in the pan for 5 minutes before serving.