Wash and dry chicken breasts.
Pound chicken to slightly flatten ~ see notes. This is optional but useful.
Add salt and pepper to flour and stir together. Pour flour onto a large plate. Coat chicken (both sides) with flour mixture.
Heat olive oil in a large skillet on medium heat. Medium -high if needed.
Place chicken breasts in skillet and cook each side until browned, about 8 minutes.
Remove chicken and set aside, covered.
Add sliced mushrooms and optional sweet pepper slices to skillet. Cook about 3 minutes.
Add wine and Dijon mustard to skillet and mix together.
Cook on low for 1-2 minutes.
Add chicken breasts to skillet and cover with the sauce.
Simmer covered for about 8 minutes. Check chicken for doneness, inside temp should be 165 degrees F.
Sprinkle chopped parsley over all before serving.