Preheat the oven to 375°F (190°C).
Place the chicken breasts and potatoes in a large bowl. Drizzle with 1 tablespoon olive oil and toss well to coat.
Season generously with salt, pepper, and Italian seasoning.
Heat a large oven-safe skillet over medium heat. Melt 2 tablespoons butter with the remaining olive oil.
Add chicken to one side of the skillet and potatoes to the other side. Cook undisturbed for 3–4 minutes.
Flip the chicken and stir the potatoes. Cook another 3–4 minutes until lightly golden.
Transfer chicken and potatoes to a plate and keep warm.
In the same skillet, melt 1 tablespoon butter. Add garlic and cook for about 1 minute until fragrant.
Stir in chicken broth and Dijon mustard.
Slowly whisk in heavy cream, salt, and cracked black pepper.
Return the chicken and potatoes to the skillet and coat them in the creamy Dijon sauce.
Transfer the skillet to the oven and bake for 15–20 minutes until the chicken is fully cooked and potatoes are fork-tender.
Spoon extra Dijon cream sauce over the chicken and potatoes before serving. Garnish with fresh herbs if desired.