Keep basic chicken scaloppine warm in a 200° oven.
Add olive oil, mushrooms, shallots, and thyme to hot pan used to cook chicken (don't wash) and stir often over high heat until mushrooms are browned, 4 to 5 minutes. Spoon over chicken.
Add sherry, chicken broth, and cream to pan; stir until mixture is boiling. Boil, stirring occasionally, until juices are slightly reduced, 1 to 1 1/2 minutes. Spoon sauce over chicken. Sprinkle with parsley and salt and pepper to taste.