Preheat the oven to 170 F (76 C) to keep the chicken warm without cooking it.
Bread the chicken cutlets in English style:
Coat them with flour and remove the excess, then dip them in the beaten egg and finish by coating them with breadcrumbs. Set aside.
In a pan, melt the butter and oil and heat well.
Add the cutlets and cook until golden brown on both sides. Remove them from the pan and put them in the oven on a plate.
In the same pan, add a little oil if needed and sauté the bell peppers, garlic, and onion for about 3 minutes.
Add the sun-dried tomatoes, shallots, and mustard.
Deglaze with white wine and reduce for 2 minutes.
Add the chicken broth and bring to a boil. Reduce the heat, add the cream, and let simmer for 5 minutes.
Cut the chicken into thick strips and serve with a generous portion of sauce.