Season the chicken breasts with salt and black pepper on both sides.
In a large skillet, heat the olive oil and butter over medium heat. Once hot, add the chicken breasts and cook for about 6-7 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, reduce the heat to low and add the heavy cream, Dijon mustard, lemon juice, garlic powder, and dried thyme. Stir to combine and let simmer for about 2-3 minutes until slightly thickened.
Pour in the chicken broth and stir well, allowing the sauce to simmer for another 2-3 minutes.
Return the chicken to the skillet, coating it in the creamy sauce. Cook for an additional 2 minutes to heat through.
Serve the chicken over a bed of mashed potatoes, drizzling the creamy Dijon sauce on top. Garnish with chopped parsley if desired.