In a large bowl, combine the dry ingredients: both flours, cornstarch, powdered sugar, baking powder, and salt. Mix to blend the ingredients evenly.
In a small bowl, stir together the coconut oil, coconut milk, and vanilla (or other flavor) extract.
Fold the liquid ingredients into the flour mixture. Stir until the cookie dough holds together. If it is too dry, add more coconut milk one tablespoon at a time, but don’t make the dough too moist or sticky.
Pull the dough into a ball and cover the bowl with plastic wrap. Refrigerate for 10 to 15 minutes.
While the dough is chilling, preheat the oven to 350°F and line the baking sheets with parchment.
Take the dough out of the fridge and place it between two sheets of parchment paper. Roll out the dough, but do not add any additional flour. Roll to a thickness of a quarter inch.
If the dough is too hard to roll, pull it out of the fridge for a few minutes to warm up, but do not let it get up to room temperature.
Once the dough has been rolled out, use a two-inch cookie cutter to cut out cookies. You can also use a biscuit cutter.
Place half of the cookies on the cookie sheet. For the other half of the cookies, use a small, round cutter (a half-inch to an inch works best) and cut a round hole in the center. Place these cookies on the cookie sheet, leaving an inch between cookies.
Take any leftover dough scraps from what you rolled out and the center pieces that you cut out, and roll it out again to make more cookies.
Once all the cookies have been cut out and are on the cookie sheet, bake for 9-11 minutes. The cookies should be lightly golden brown around the edges.
Let the cookies cool on the baking sheet for 5 minutes and then transfer to a wire rack.
After the cookies are fully cooled, dust the cookies with the cut-out with powdered sugar.
Flip the cookies without a cut-out center over so the bottom of the cookie is facing up. Put 1 teaspoon of jam on those cookies, and then place one of the cut-out cookies on top, with the powdered sugar side up. Lightly press the top down to make a sandwich cookie.