Combine the softened unsalted butter, grated Parmesan cheese, salt, and all-purpose flour in a mixing bowl until crumbly.

Add the egg and mix until a smooth, cohesive dough forms.

Roll the dough quickly onto a baking tray to a rough flat layer. Cover it tightly with plastic wrap.

Refrigerate the covered dough for 120 minutes until firm.

Roll the chilled dough to a 3–4 mm thickness. Cut it into small shortbread shapes.

Arrange the shapes on the baking tray and chill them briefly until firm.

Bake the shortbread at 160°C / 320°F for 12 minutes, until lightly golden at the edges.

Remove the Parmesan shortbread from the oven and let it cool completely.

Dice the cooked red beetroot into small pieces. Transfer it to a saucepan.

Add the water, sherry vinegar, and star anise to the saucepan. Simmer for a few minutes.

Remove and discard the star anise. Blend the beetroot mixture until very smooth.

Pass the beetroot purée through a fine sieve. Return the smooth purée to the saucepan.

Stir ground cumin, sumac, balsamic vinegar, and agar-agar into the beetroot purée. Bring the mixture to a boil.

Boil the beetroot mixture for 30 seconds while stirring. Pour it in a thin layer into a shallow tray.

Let the beetroot jelly set until firm. Cut it into small squares.

Place one beetroot jelly square on each cooled Parmesan shortbread. Serve immediately or chilled.