Preheat oven to 375°F.
In a large bowl, combine chicken and potatoes. Drizzle with 1 tablespoon olive oil, toss to coat, then season with salt, pepper, and Italian seasoning.
In a large skillet, melt 2 tablespoons butter with 1 tablespoon olive oil over medium heat. Add chicken to one half of the pan and potatoes to the other. Cook for 3-4 minutes on each side until browned.
Transfer chicken and potatoes to a plate and cover to keep warm.
In the same skillet, melt 1 tablespoon butter. Add garlic and sauté until fragrant, about 1 minute.
Stir in chicken broth and Dijon mustard, then whisk in heavy cream, salt, and pepper.
Return chicken and potatoes to the skillet, tossing them in the sauce.
Transfer skillet to the oven and bake for 15-20 minutes, until chicken is cooked through, and potatoes are tender.
Garnish with cracked black pepper and fresh herbs if desired.