Preheat oven to 200 degrees. Place meat between two pieces of plastic wrap, and lightly pound until 1/3 inch thick. Season both sides of pork with salt and pepper.
In a large skillet, heat 1 tablespoon of butter over medium-high heat. Working in batches, add pork, and cook until browned, about 2 minutes per side. Transfer to a platter, and keep warm in the oven. Add more butter to skillet as needed. Reduce heat to medium if the pan begins to smoke, or if the browned bits on the bottom of the pan begin to burn.
Reduce heat to medium, and add 2 tablespoons butter to the skillet. When melted, add mushrooms and celery. Season with salt and pepper. Cook, stirring occasionally, until pan is dry and mushrooms are beginning to brown, about 5 minutes.
Add stock, and cook, scraping up browned bits from bottom of skillet with a wooden spoon. Continue to cook until sauce is reduced and thickened, 3 to 4 minutes. Stir in cream and parsley. Taste, and adjust for seasoning. Pour sauce over pork, and serve immediately.