In a large mixing bowl, use an electric mixer to cream together the softened 8 ounces (2 sticks) unsalted butter, 1 cup packed light brown sugar, and 1 cup of the white granulated sugar on medium-high until the mixture is light and fluffy, about 2 minutes.
Add the 2 large eggs and 1 teaspoon vanilla extract to the butter mixture and mix until incorporated.
Add 1 cup of the creamy peanut butter to the bowl and mix until blended. Reserve the remaining 1/2 cup of peanut butter for filling and decorating.
In a separate bowl, whisk together 2 1/2 cups all-purpose flour, 1 teaspoon baking soda, 1 teaspoon baking powder, and 1 teaspoon salt.
Add the dry ingredients to the wet ingredients and mix until just combined and a dough forms. Do not overmix.
Cover the bowl and refrigerate the dough for 30 minutes.
After chilling, preheat the oven to 350°F and line a large baking sheet with parchment paper.
Portion the chilled dough into 75-gram or 1/4-cup portions. Roll each portion into a round, smooth ball using the palms of your hands.
Press your thumb into the center of each dough ball to create a large crater. Put about 1 teaspoon of the reserved peanut butter into each crater, then pinch the opening closed so the peanut butter is enclosed.
Roll each filled ball through the remaining 1/2 cup of white granulated sugar until the surface is completely coated.
Gently press each sugared ball between your hands to flatten it slightly into a disk.
Place the cookies on the prepared baking sheet about 4 to 4 1/2 inches apart.
Bake at 350°F for 11 to 13 minutes for slightly underdone centers, or 13 to 15 minutes for firmer, more well-done cookies.
Remove the baking sheet from the oven and let the cookies cool on the sheet for 5 minutes, then transfer them to a wire rack to cool until warm or completely at room temperature.
When the cookies are warm or cooled to room temperature, put any remaining reserved peanut butter into a sandwich-size Ziplock bag, seal the bag, and cut the smallest hole possible in one corner. Squeeze the peanut butter through the hole to pipe zig-zag lines across the top of each cookie.
Serve the cookies warm or at room temperature.