For the cookies:
2 1/2 cups all-purpose flour
1 teaspoon baking soda
3 teaspoons baking powder
1 teaspoon kosher salt
1 cup unsalted butter (2 sticks), at room temperature
1 1/2 cups dark brown sugar
3/4 cup granulated sugar
2 large eggs, at room temperature
1 teaspoon pure vanilla extract
1 cup crunchy peanut butter
2 cups quick-cooking oats
For the filling:
1/2 cup unsalted butter (1 stick), at room temperature
1 cup crunchy peanut butter, at room temperature
1/2 cup powdered sugar, sifted
To make the cookies:
1 Preheat the oven to 350°F. Arrange a rack in the upper third of the oven, and another in the bottom third. Line 2 baking sheets with parchment paper or silicone mats.
2 In a large bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
3 Using a mixer fitted with the paddle attachment, cream the butter. Beat in the dark brown and granulated sugar for about 5 minutes or until very pale, light, and fluffy. Beat in the eggs one at a time, mixing well after each. Stir in the vanilla extract. Stir in the peanut butter. Reduce the mixer speed to low and add the flour mixture, beating until just combined, 5 to 10 seconds. Add the oats. Be careful not to overmix the dough.
4 Scoop out 2 ounces of cookie dough and roll into balls with your hands. Using the bottom of a tumbler or other glass, flatten the cookie-dough balls into 1/2-inch high circles. Arrange the disks on the prepared baking sheets about 2 inches apart. Refrigerate for about 30 minutes.
To make the filling and assemble the cookies:
1 Using a mixer fitted with the paddle attachment, cream the butter with the peanut butter for about 5 minutes on medium speed. Reduce the speed to low and add the sifted powdered sugar, mixing until well combined. Scrape the filling into a large zipper-top or pastry bag and set aside.
2 Bake the cookies until they’re a light golden brown, 8 to 10 minutes, rotating the baking sheets halfway through. Let the cookies rest on their baking sheets for 10 minutes, then transfer directly to wire racks to cool completely.
3 Once the cookies have cooled completely, turn over half the cookies, flat side up. If you’re using the zipper-top bag for piping, snip off a small tip of one of the bottom corners. Pipe about 1 tablespoon of the filling on cookies sitting flat side up. Place the remaining cookies on top and gently press to squeeze the filling out to the edges. Serve, or store in an airtight container at room temperature for up to 3 days.