1. Preheat oven to 375°. Whisk together first 4 ingredients in a medium-size mixing bowl. In a separate bowl, beat together granulated and brown sugars, butter, and 1/4 cup peanut butter until light and fluffy. Add vanilla and egg, beating to combine. Stir in dry ingredients, blending well. Set dough aside.
2. Stir together remaining 3/4 cup peanut butter and powdered sugar until smooth. With floured hands, roll mixture into 26 (1-inch) balls.
3. Break off about 1 tablespoon cookie dough; make an indentation in center with thumb, and press 1 peanut butter ball into indentation. Wrap dough up and over filling, pressing to seal; roll cookie to smooth it out. Repeat for each cookie.
4. Dip top of each cookie in granulated sugar, and place 2 inches apart on lightly greased baking sheets. Use greased bottom of drinking glass to flatten each cookie to about 1/2 inch thick.
5. Bake cookies at 375° for 7 to 9 minutes or until set. Let cool on wire rack.