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.