Preheat oven to 350°.
In a small bowl, whisk flax and water. Let it rest a few minutes to thicken.
In a medium bowl, whisk the flour, baking powder + salt.
In a small saucepan over medium-low heat, add butter and 1/2 cup peanut butter, continuing to stir until melted.
Add both sugars, flax mixture + vanilla to saucepan, stirring until incorporated. Fold in the flour mixture.
Press mixture evenly across the lined baking sheet. Bake for 18 - 22 minutes, until center is set. Remove from oven and spread remaining peanut butter evenly across crust. Let it rest and cool completely.