Preheat oven to 375°F.
In a large mixing bowl, toss quartered potatoes andchicken thighs with 1 tablespoon of the olive oil, Italian seasoning, salt, and pepper.
In a large, heavy oven-safe skillet, add remaining olive oil and 1 tablespoon of the butter over medium-high heat. Add the chicken and potatoes, and cook without disturbing for about 4-5 minutes, or until chicken is browned on the one side.
Carefully flip the chicken over to brown on the other side, and give the potatoes a stir.
Remove chicken and potatoes and cover to keep warm while you make the sauce.
To make the sauce, add more butter to the skillet if necessary. Add the garlic and stir until fragrant, about one minute. Then add the cream, chicken stock, and Dijon mustard. Stir, scraping up all the browned bits from the bottom of the pan.
Once the sauce is mixed, add back the chicken and potatoes, stirring so that every bit of chicken and potatoes is coated in the sauce.
Put the whole skillet in the oven, uncovered, for about 15-20 minutes or until chicken is cooked and potatoes are fork-tender.
Serve the chicken and potatoes with extra sauce spooned over, accompanied by a simple salad or a steamed vegetable.