1 cup butter, softened
1 cup brown sugar
1 cup white sugar
1 egg
1 tablespoon vanilla extract
1 1/2 cups all-purpose flour
1 cup milk
Preheat the oven to 375 degrees F (220 degrees C). Grease cookie sheets.
In a large mixing bowl, cream together the butter, brown sugar, white sugar and egg until smooth. Mix in the flour, then fold into the creamed mixture until well blended. Shape the mixture into a 1/4-inch diameter oval.
Spread a wrapped pan inside the prepared cookie sheet. Bake for 8 to 10 minutes in the preheated oven, turning once, until edges are light brown. Remove from cookie sheets and cool on wire rack.
While the peaches are heating, preheat the oven to 425 degrees F (220 degrees C). Transfer peaches to a medium baking sheet and cover with waxed paper. Brush the peaches with the egg and vanilla drippings while still warm.
Bake peaches in the preheated oven for 20 to 25 minutes in the preheated oven, until peaches are golden brown and tender. Remove from hot oven and cool completely.
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