Sprinkle chicken with salt and pepper. Heat 2 tsp olive oil in a large skillet over medium heat. Cook the chicken, turning once until browned and just cooked through, 7-10 minutes total. Transfer to a plate.
Add 1 1/2 tsp oil and mushrooms to the pan; cook, stirring occasionally, until the liquid has evaporated and mushrooms are browned. Increase heat to high. Add wine and cook until it has mostly evaporated, about 4 minutes.
Reduce heat to medium. Stir in half and half and any accumulated juices from the plate the chicken is on, stir in salt and pepper to taste. Return chicken to pan and turn to coat with the sauce.
Serve the chicken over egg noodles (optional) with sauce and sprinkled with parsley.