Preheat oven to 350 degrees F.
Pound breasts lightly with meat mallet to a consistent thickness. Season well with salt and pepper. In a 10-inch to 12-inch saute pan, heat butter over medium heat until foam subsides. Add pheasant breasts, skin down, and cook until golden brown, about 8 to 10 minutes. Place pan in oven 8 to 10 minutes. Remove pan from oven and breasts from pan.
Add shallots to pan and stir. Cook over medium heat until softened, about 4 to 5 minutes. Add cider vinegar and apples and cook until vinegar dissipates by half. Add stock and cream and bring to a boil. Return pheasant breasts to pan and cook until sauce is reduced by half. Season with salt and pepper and serve immediately. Spoon sauce over and sprinkle with pomegranate seeds.
Recipe courtesy of Mario Batali