Season the chicken breasts with Italian seasoning, salt, and pepper.
Heat a skillet over medium heat, then add 1 tbsp. of butter and 1 tbsp. of olive oil. Allow the butter to melt.
Add the chicken breasts and halved potatoes to the skillet. Cook for about 5 minutes, flip the chicken, and cook for another 5 minutes, or until both the chicken and potatoes are nicely browned.
Remove the chicken and potatoes from the skillet and set them aside.
Preheat the oven to 370°F.
In the same skillet, add 1 tbsp. of butter and let it melt. Add the minced garlic and sauté for 30 seconds.
Stir in the chicken broth, Dijon mustard, salt, and pepper. Whisk in the heavy cream until the sauce is well combined.
Return the chicken and potatoes to the skillet, ensuring they are coated with the sauce.
Transfer the skillet to the oven and bake for 20 minutes, or until the chicken and potatoes are fully cooked through.
Garnish with fresh parsley and serve.