Position oven racks in the center and top third of the oven and preheat to 350 F. Line two baking sheets with parchment paper or silicone baking mats.
Mix together the rice flour, cornstarch, tapioca starch, baking powder, baking soda, and salt. Set aside.
Using an electric mixer at high speed, beat the shortening/butter in a large bowl until smooth. Gradually beat in the brown sugar, then the egg and oil, beating well after the addition of each. Add the peanut butter and vanilla and beat, scraping the sides of the bowl often, until the mixture is paler, about 2 minutes. Reduce the mixer speed to low. Add the flour mixture and mix just until combined.
Using a level tablespoon of dough for each cookie, roll the dough into balls. Place 1 inch apart on the baking sheets. Using your thumb, make a deep indentation in the center of each ball. Use a ½ teaspoon to spoon the preserves into the indentation.
Bake until the cookies are lightly browned around the edges, switching the positions of the sheets from top to bottom and front to back halfway through baking, 12 to 15 minutes. Cool on the sheets for a few minutes, then carefully transfer to a wire cake rack to cool completely. The cookies can be stored in an airtight container at room temperature for up to 5 days.