Preheat your oven to 375 degrees Fahrenheit.
Season both sides of the chicken breasts with Italian seasoning, salt, and pepper. Cook in a mix of butter and olive oil until golden brown.
In the same pan, add halved baby potatoes, more butter, and minced garlic; sauté until they begin to soften.
Pour in chicken broth and Dijon mustard; stir well while scraping up any browned bits from the bottom of the pan.
Lower heat and whisk in heavy cream along with additional salt and cracked black pepper; simmer until thickened.
Return chicken breasts to the pan with potatoes; bake in the preheated oven until chicken is cooked through.