French Chicken with Vermouth Sauce

Ingredients

• 2 tablespoons butter
• 4 pounds boneless chicken thighs
• salt
• freshly ground black pepper
• 1 medium onion, finely chopped
• 1 medium carrot, finely chopped
• 1/2 rib celery, finely chopped
• 2 ounces prosciutto or country ham, finely chopped
• 3/4 cup Vermouth
• 3/4 cup homemade or low-salt canned chicken stock
• 3 tablespoons heavy cream, at room temperature
• Chopped fresh flat-leaf parsley
• 2 cups rice for serving with chicken