Preheat your oven to 375°F (190°C).
In a large oven-safe skillet, heat the olive oil over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Sear the chicken for about 4-5 minutes on each side until golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, reduce the heat to medium and add the minced garlic. Sauté for about 30 seconds until fragrant.
Stir in the Dijon mustard, heavy cream, chicken broth, and thyme. Bring the mixture to a gentle simmer.
Layer the sliced potatoes evenly over the cream mixture in the skillet. Place the seared chicken on top of the potatoes.
Sprinkle the Gruyère cheese and Parmesan cheese over the chicken and potatoes.
Cover the skillet with a lid or aluminum foil and bake in the preheated oven for 30 minutes.
Remove the lid or foil and bake for an additional 15-20 minutes, or until the potatoes are tender and the cheese is golden and bubbly.
Let it cool for a few minutes before serving.