In a medium saucepan over low heat, heat the half-and-half, gelatin, and sugar for about 8-10 minutes, stirring frequently, until all the sugar is dissolved and steam starts to form. Do not boil.
Remove from the heat and cool for about 5 minutes. With a wire whisk, stir in the sour cream and the extracts and combine thoroughly. Pour into a 9-inch glass pie plate and chill for 2-3 hours. Top with the sliced peaches and serve.