In a stand mixer, cream together butter and sugar until smooth and fluffy. Add in eggs and egg white, a little at a time, beating well between each addition. Add vanilla extract, and mix until well incorporated and smooth.
Mix flours, tapioca starch, xanthan gum, baking powder, ans salt together. Carefully mix dry ingredients into wet ingredients until fully incorporated. Wrap dough in plastic film, chill for 1 hour.
Preheat oven to 400 F (200 C), line baking sheets with parchment paper.
Dust work surface generously with corn starch, roll cookie dough out to about 1/4" thick (can be slightly thicker).
Use cookie cutters to cut out 3" scalloped rounds, place cookies 2" apart on prepared baking sheets.
Bake cookies for 8-10 minutes, or until bottoms look lightly golden.
Allow cookies to cool on baking sheets for at least 5 minutes before moving. Cookies need to cool completely before sandwiching.
While waiting for the cookies to cool, make your glaze: Use a fork to whisk together icing sugar and salt. Add almond extract and enough hot water to make a thin glaze.
Flip half of the cookies over, spread underside with jam. Top each with one of the remaining cookies.
Spread top of each cookie sandwich with glaze, place a dot of red frosting (dyed remaining glaze), gel icing, or a piece of cherry while glaze is still wet.
Allow cookies to sit, undisturbed, until set.