Preheat oven to 325º F and line a baking sheet with a silicone mat or parchment paper.
In a medium bowl, stir oats, flour, baking powder, and salt together until well combined. Set aside.
In a separate bowl, beat softened butter and brown sugar together until creamy. Mix in egg and vanilla. Stir in dry ingredients until just incorporated, and then fold in chopped peaches.
Drop spoonfuls of the dough, about the size of walnuts onto the lined baking sheet. Bake for 13-15 minutes, or until lightly browned. Remove from oven, and let cool about 15 minutes before transferring to wire rack to cool completely.
To prepare icing: Combine all icing ingredients, adding cream or milk to achieve desired consistency. Drizzle or spread icing over warm cookies.
Makes about 1 dozen cookies
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