For the Poppy Seed Shortbread Base:
Grate the marzipan. In a stand mixer, beat 150 g butter and 50 g marzipan until smooth, gradually add 75 g powdered sugar, salt, and half the almond essence. Whip for an additional 2 minutes.
Combine 200 g flour, 50 g cornstarch, and 50 g ground poppy seeds. Beat an egg into the butter mixture, then add the dry ingredients and mix until combined.
Transfer the dough onto cling film, shape into a disk, and refrigerate for 2 hours.
For the Piped Upper Part:
4. Preheat oven to 190°C (375°F). Line cookie sheets with parchment paper.
5. Beat remaining butter with leftover marzipan. Add 80 g powdered sugar, a pinch of salt, remaining almond essence, and vanilla. Beat in the second egg.
6. Mix remaining flour and ground poppy seeds, add to the batter with milk and 1 tbsp rum. Beat until smooth.
7. Transfer the batter to a piping bag with a star nozzle and pipe circles onto prepared parchment paper.
8. Freeze each tray for 8 minutes before baking for 10 minutes at 190°C. They should not brown much.
9. Roll out chilled shortbread dough, cut rounds using the same cookie cutter, and bake on lined trays at 175°C (350°F) for 8 minutes.
10. Let cookies cool. Whisk jam with remaining rum and spread about 1/2 tsp on each shortbread base. Top with a piped cookie and press gently to adhere.