Peanut Stars Sandwich Cookies

Makes about 2 dozen sandwich cookies.
Taste Tip: This dough must be prepared in advance. Shelf-stable peanut butter, such as Jif or Skippy brands, works best, due to its salt and sugar content. Both raw or roasted peanuts are suitable, and both are better when toasted. Place peanuts in a dry skillet over medium heat, and cook, stirring or shaking the pan frequently, until they just begin to release their fragrance, about 4 to 5 minutes (or preheat oven to 325 degrees, spread nuts on an ungreased baking sheet and bake, stirring often, for 5 to 7 minutes). Remove from heat and cool to room temperature.
For cookies
1¼ cups roasted, unsalted peanuts, toasted (see Taste Tip)
¾ cup flour
1 teaspoon baking soda
½ teaspoon salt
3 tablespoons unsalted butter, melted
½ cup creamy peanut butter
½ cup granulated sugar
½ cup packed light brown sugar
3 tablespoons whole milk
1 egg
For filling
¾ cup creamy peanut butter
3 tablespoons unsalted butter
1 cup powdered sugar
1 teaspoon peeled and freshly grated ginger
Directions
To prepare cookies:
In a food processor, pulse peanuts until finely chopped and they resemble coarse crumbs (alternately, chop peanuts very fine), and reserve.
In a medium bowl, whisk together flour, baking soda and salt, and reserve.
In a bowl of an electric mixer on medium-high speed, beat butter, peanut butter, granulated sugar and light brown sugar until smooth, about 2 minutes. Add milk and egg, and beat until thoroughly combined. Reduce speed to low, add flour mixture and mix until just incorporated. Fold in peanuts. Cover with plastic wrap and refrigerate at least 1 hour.
When ready to bake, preheat oven to 350 degrees and line baking sheets with parchment paper. Roll dough into ½-inch balls and place 2 inches apart on prepared baking sheets. Using moistened fingers, gently flatten cookies into 1-inch discs.
Bake until edges are slightly browned, 10 to 13 minutes. Remove from oven, cool 2 minutes and transfer cookies to a wire rack to cool completely.
To prepare filling:
Place peanut butter and butter in a small microwave-safe bowl. Cook until mixture is easily stirred, about 30 seconds. Add powdered sugar and ginger and mix until filling is smooth.
To assemble cookies: Spread 1 teaspoon filling on the bottom of a cookie. Top with another cookie, bottom side up as if making a sandwich, and gently press cookies together. Repeat until all cookies form sandwiches.
2012 Finalist: John Halstrom and Trevor Howe of Minneapolis, Minnesota