Season the chicken breasts evenly with salt and black pepper on both sides.
Heat olive oil in a large skillet or Dutch oven over medium-high heat.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside.
Reduce the heat to medium. Add the minced garlic to the skillet and sauté for about 1 minute until fragrant, stirring constantly to avoid burning.
Pour in the chicken broth and stir to deglaze the pan, scraping up any browned bits from the bottom.
Add the heavy cream, Dijon mustard, dried thyme, and dried rosemary to the skillet. Stir well to combine and bring the sauce to a gentle simmer.
Allow the sauce to simmer for 5 minutes, stirring occasionally until it thickens slightly.
Stir in the grated Parmesan cheese until melted and the sauce is creamy.
Return the cooked chicken breasts to the skillet, spoon some sauce over them, and cook for an additional 3-4 minutes to heat through.
Sprinkle the chopped fresh parsley over the chicken and sauce before serving.