To toast the peanuts, adjust an oven rack to the center position and preheat the oven to 350°F. Put the peanuts on a large baking sheet, drizzle them with the oil, sprinkle with the salt, and toss to coat them. Spread the peanuts out in an even layer and toast them on the center rack of the oven until they are dark mahogany in color, 18 to 20 minutes, shaking the pan occasionally and rotating the pan front to back halfway through the toasting time so the peanuts brown evenly. Remove the baking sheet from the oven and set aside to cool the nuts to room temperature.

Turn off the oven. To make the dough, whisk the eggs and vanilla together in a small bowl. Combine the all-purpose and sorghum flours in a medium bowl and stir with a whisk to combine.

Put the butter in a stand mixer fitted with the paddle and beat at medium speed until the butter is softened but still cold, 3 to 4 minutes. Add the peanut butter, granulated sugar, and brown sugar and beat on medium speed until the mixture is light and fluffy, 3 to 4 minutes. Add the baking soda, salt, and baking powder and beat on medium speed for about 15 seconds to incorporate the additions. Gradually add the egg/vanilla mixture, mixing until the egg is completely incorporated. Add the combined flours and mix on low speed for about 30 seconds until no flour is visible. Cover the bowl with plastic wrap and refrigerate until the dough is chilled and firm, at least 30 minutes.

Adjust the oven racks so one is in the top third and the other is in the bottom third of the oven and preheat the oven to 375°F. Line two large baking sheets with parchment paper.

To finish the cookies, pour the granulated sugar into a small bowl. Remove the dough from the refrigerator. Scoop the dough into 21-gram (1½-tablespoon) portions and roll each portion into a ball. Roll the balls in the sugar to coat them and place 12 cookies on each of the prepared baking sheets, leaving at least 1½ inches between them. Press your thumb in the center of each ball of dough and turn your thumb to expand the divot slightly. Spoon 1 teaspoon of peanut butter into each divot and sprinkle a generous pinch of flaky sea salt on top.

Place one baking sheet on each oven rack and bake the cookies for 4 minutes. Remove the baking sheets from the oven and pile a mound of peanuts in the center of each cookie. Return the baking sheets to the oven, switching racks and rotating the sheets front to back, and bake the cookies until they are golden brown, 4 to 5 minutes. Remove the cookies from the oven. Allow the cookies to cool completely before removing them from the baking sheet.