Saute the onion butter and olive oil until soft. Combine with remaining ingredients except chicken. Season highly.
Place each breast skin side up on a board and trim away fat. Loosen skin from one side of the breast and stuff approximately 1/3 cup filling under the skin. Tuck the skin and meat under the breast, forming an even, round, dome shape. Place in a buttered dish.
Fifteen minutes before baking, preheat oven to 350-degrees. Bake breasts until golden brown about 30-35 minutes. Don't overcook or chicken will be dry.
Cool slightly before serving, and cool to room temperature if you are going to slice into smaller serving pieces. Arrange on platter and garnish with fresh herbs and cherry tomatoes.