Preheat your oven to 375 degrees Fahrenheit to ensure it's ready for baking.
Prepare the chicken and potatoes: In a large bowl, combine the chicken and potatoes. Drizzle with olive oil, then season with salt, pepper, and Italian seasoning or Herbs de Provence. Toss to coat evenly.
Cook chicken and potatoes: In your skillet, melt butter over medium heat, then add olive oil. Place chicken on one side and potatoes on the other. Cook for 3-4 minutes, then flip the chicken and cook for another 3-4 minutes. Remove from the skillet and keep warm.
Make the dijon cream sauce: In the same skillet, add more butter and cook the garlic until fragrant. Stir in chicken broth and dijon mustard, then whisk in heavy cream, salt, and pepper.
Combine and bake: Return the chicken and potatoes to the skillet, tossing them in the sauce. Transfer to the oven and bake for 15-20 minutes, until the chicken is cooked through and the potatoes are tender.
Serve: Spoon the dijon sauce over the chicken and potatoes, garnish with cracked black pepper and fresh herbs if desired.