cook's illustrated's peanut butter sandwich cookies

1 1/4 cups raw peanuts
toasted and cooled
3/4 cup flour
1 tsp baking soda
1/2 tsp salt
3 tbsp unsalted butter
1/2 cup creamy peanut butter
with salt
1/2 cup sugar
1/2 cup light brown sugar
3 tbsp whole milk
1 whole egg
3/4 cup creamy peanut butter
with salt
3 tbsp unsalted butter
1 cup confectioner's sugar
aka powdered sugar
If you liked Nutter Butter as a kid, this cookie is a grown-up version of it. This Cook's Illustrated recipe showcases delicious, unprocessed peanut butter flavor and pairs it with a nice crunchy texture. We went through a whole carton of whole milk (gasp) eating up these cookies. These are the best peanut butter cookies we've ever had! Adapted from the March/April 2012 issue of Cook’s Illustrated.
Move oven racks to the 1/3 and 2/3 levels in the oven, then preheat oven to 350°F. Line 2 cookie sheets with parchment paper.
With a food processor or a magic bullet, bring the peanuts to a fine chop, about 10 pulses.
Whisk dry ingredients - flour, baking soda, and salt - together in a bowl.
In a separate, larger bowl, whisk together the butter, peanut butter, sugar, brown sugar, milk, and egg. Combine the contents from the first bowl of dry ingredients into this larger bowl. Then mix in the peanuts.
Measure out 12 tablespoon mounds on each cookie sheet. Space them out evenly, and then flatten to a 2-inch diameter with a wet palm.
Bake the cookies for about 8 minutes, then switch the rack positions of the cookie sheets and bake for another 8 minutes. Cookies should be firm to touch and golden brown.
Let the cookies cool on the cookie sheet for about 5 minutes, then transfer them to cooking racks and allow them to cool for about 30 minutes.
Soften the peanut butter and melt the butter together in the microwave for about 30-40 seconds. Stir to combine, and then stir in the powdered sugar.
Assemble the cookies by placing 1 tablespoon of filling into the center of a cookie. Press together with a second cookie to evenly spread out the filling until it reaches the edges. Repeat. Set the filling for at least an hour before serving. Cookies will keep for 3 days in an airtight container.