In the bowl of an electric mixer, cream the butter, 1/2 cup of powdered sugar and the granulated sugar until light and fluffy, about 4 minutes.
Add in the egg and mix well.
Add in the sourdough discard and vanilla and almond extracts.
Mix in the flour, almond flour and salt and combine until just blended through.
Chill the dough for at least one hour.
Preheat oven to 350 and line two baking trays with parchment paper.
Working with half the dough at a time, roll the dough out on a well floured surface until about 1/4" thick. The dough is soft and sticky, so use well floured counter, ensuring the dough does not stick, and flour your rolling pin as well.
Cut desired shapes, making sure you cut a smaller hole in the center of half of the cookies to act as a lid.
Carefully transfer the cut shapes to the prepared pans and bake for 8-12 minutes, until just starting to turn golden on the edges.
Allow the cookies to cool on the pan for 5 minutes before transferring to a wire rack to cool completely.
Dust the cookie tops with the remaining powdered sugar.
Spoon the jam into a bowl and stir it vigorously to thin it out and make it spreadable. Spoon small amounts into the center of each cookie bottom and place a top cookie on top.
Notes
Store cookies in an airtight container on the counter for 3-5 days.