Step 1Heat the oven to 375 degrees. Set aside 2 ungreased baking sheets.
Step 2Use a mixer to cream the granulated and brown sugars and butter. Add the egg white and vanilla; mix well. Add the peanut butter; mix until smooth. Use a wooden spoon to stir in the flour, baking soda and salt; mix just until the flour disappears. Do not overmix.
Step 3Use a pastry bag fitted with a 1/3-inch wide tip to pipe out 1-inch diameter rounds, spacing them 2 inches apart, on the baking sheets. Alternately, use 1 teaspoon of batter for each cookie. Top each with a peanut half.
Step 4Bake until set and just slightly browned, about 7 to 8 minutes. Let the cookies rest 3 minutes, then use a metal spatula to transfer them to a wire rack to cool completely. Store in an airtight container for several days at room temperature or freeze up to 1 month, wrapped airtight.