In a small bowl, whisk together eggs and vanilla. In a medium bowl, whisk together all-purpose flour and sorghum flour.
Add butter to a stand mixer fitted with paddle attachment; beat on medium speed until butter is softened but still cold, 3–4 minutes, scraping down and bottom of bowl as needed.
Add peanut butter, granulated sugar and brown sugar; beat on medium until mixture is light and fluffy, 3–4 minutes, scraping down sides and bottom of bowl as needed.
Add baking soda, salt and baking powder; beat on medium for about 15 seconds to incorporate. Stop mixer and scrape down bowl and paddle. With mixer on medium, gradually add egg/vanilla mixture, mixing until egg is completely incorporated. Scrape down bowl.
Add flour mixture and mix on low for about 30 seconds until combined. Using a spatula. Give dough one more mix, ensuring no dry ingredients are at bottom of bowl.
Cover with plastic wrap and refrigerate until dough is firm, at least 30 minutes.
Heat oven to 375ºF with racks set in upper-middle and lower-middle positions. Line two half sheet pans with parchment paper.