Preheat oven to 375º F. Place each breast between 2 sheets of waxed paper or plastic wrap; pound lightly to ¼ inch thickness. Season each side with salt and pepper.
Divide the pepper strips and thyme between the chicken breasts, reserving some to garnish with. Carefully roll up chicken and secure with toothpicks.
Add oil and butter mixture to an oven-safe skillet. Sear each side of chicken for 2-3 minutes. Place the skillet in the oven for 10-15 minutes until the chicken is no longer pink inside.
Take the chicken out of the skillet and return it to the stove on medium heat. Add chicken broth and bring to a boil. Stir in the Dijon mustard and continue stirring for 2 minutes or until slightly reduced. Spoon over chicken and garnish with remaining peppers.