Heat a large skillet over medium-high heat and add olive oil and butter. Once melted, cut chicken breasts in half and dredge in flour, shaking off excess. Fry the chicken cutlets for about 5 minutes per side.

In the same skillet, lower the heat and add fresh rosemary. Sauté for about 1 minute until fragrant, scraping the bottom of the pan for flavor.

Pour in white wine to deglaze the skillet, then stir in minced garlic and Dijon mustard, cooking until the mixture is smooth and begins to thicken.

Reduce heat to medium-low, stir in heavy whipping cream, and return chicken to skillet. Simmer for 8-10 minutes until chicken absorbs flavor and sauce thickens.

Season with salt and pepper, stir, and serve hot with sauce spooned over the chicken.