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

In a large bowl, cream together 1 cup softened butter, 1 cup peanut butter, granulated sugar, and brown sugar until light and fluffy.

Add eggs one at a time, followed by vanilla extract, mixing well after each addition.

In a separate bowl, whisk together flour, baking powder, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients until a thick dough forms.

Scoop 1/3 cup portions of dough, roll into balls, and place on baking sheets spaced 3 inches apart.

Bake for 10 to 12 minutes until the edges are just set but the centers remain soft; do not overbake.

Allow cookies to cool completely on the baking sheet to firm up before frosting.

To make the frosting, cream 0.5 cup butter and 0.5 cup peanut butter together, then gradually add powdered sugar and milk until smooth and pipeable.

Pipe a thick ring of peanut butter frosting onto the perimeter of each cooled cookie and fill the center with a generous dollop of grape jelly.