1.Melt butter and oil in a large nonstick skillet over medium high heat.
2.When foaming add chicken breasts and sprinkle with salt and pepper to taste. Cook until golden and just tender about 5 minutes per side. Be careful not to cook to high to fast so adjust your pan temp accordingly. Remove chicken from pan when done.
3.Pour off excess fat from pan and turn heat on pan to medium low heat. Add the shallots and cook for about 1 to 2 minutes until translucent. Add the mustard and cream to the pan and raise heat to medium. Scrape up brown bits as you stir with a spoon. Cook until thickened and mixed about 2 to 3 minutes. Taste and adjust seasoning to taste.
4.Return chicken to the pan and coat with sauce. Transfer to serving dish or individual plates and sprinkle with parsley. Serve at once.