Begin by heating a large skillet over medium heat and adding the olive oil. Once shimmering, it indicates the oil is hot enough.

Generously season your chicken pieces with salt and black pepper. Place the seasoned chicken in the skillet in a single layer, and sear them for 5-6 minutes on each side until they develop a golden-brown color.

Carefully remove the chicken from the skillet and transfer it to a plate. Let it rest while you prepare the sauce.

In the same skillet, lower the heat slightly and add the Dijon mustard and heavy cream. Stir vigorously to combine, and simmer this mixture for about 2-3 minutes until the sauce thickens slightly.

Gently return the chicken pieces to the skillet, ensuring they are coated in the creamy mustard sauce. Cover the skillet and let it cook for approximately 30 minutes on medium-low heat.

After 30 minutes, check that the chicken is fully cooked and tender. Serve your delightful French Mustard Chicken hot, garnished with fresh herbs if desired.