Grind the oats in a food processor into a fine powder. Finely grind the dry-roasted peanuts separately. Set both aside.

In a medium bowl, whisk together the flour, ground oat powder, baking soda, baking powder, and salt.

In a large bowl using an electric mixer, cream the softened butter, 1/2 cup peanut butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.

Beat in the egg and vanilla extract until well combined.

With the mixer on low, gradually add the dry ingredients until just combined. Mix in the finely ground peanuts.

Wrap the dough in plastic and refrigerate for at least 1 hour.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Shape the dough: Roll 1 tablespoon of dough into a 2-inch log. Place on sheet, press with a fork to create a cross-hatch, and pinch the center to form a peanut shape. Repeat, spacing 2 inches apart.

Bake for 9-11 minutes, until edges are lightly golden. Cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.

For the filling, beat 1/2 cup butter and 1 cup peanut butter until smooth. Gradually beat in powdered sugar, then vanilla and cream until light and fluffy.

Spread or pipe filling onto the flat side of half the cookies. Top with remaining cookies to form sandwiches.