Place a rack in the middle of the oven. Preheat the oven to 350ºF (180ºC). Line a 13x9-inch nonstick baking sheet with parchment paper.
2
In a medium bowl, beat the peanut butter, sugar, eggs and vanilla with an electric mixer on low speed until well blended. Add the chickpea flour, xanthan gum and salt and beat on low speed until well blended. Shape half of the dough into twelve 1 inch balls and place 2 inches apart on the baking sheet. Flatten each ball to ½-inch thick by making criss-cross marks with the tines of a fork.
3
Bake until the cookies are lightly browned and firm, about 12 to 15 minutes. Cool the cookies on the pan on a wire rack for 10 minutes. Transfer the cookies to the wire rack to cool completely. Repeat with remaining dough.