Proof the yeast: In a small bowl, dissolve the yeast in the lukewarm water and sugar. Let it stand for 10 minutes, until a bubbly foam forms on the surface. This indicates that the yeast is active and ready to use.
Mix the dry ingredients: In a large bowl, combine the flour, anise seeds, salt, and sugar. Mix well.
Add the oil: Gently warm the sunflower oil and add it to the flour mixture.
Make the dough: Add the lukewarm water and proofed yeast to the flour mixture. Knead until you have a soft, pliable dough. Cover the bowl with a clean kitchen towel and let the dough rise for 1 hour, or until doubled in size.
Prepare the filling: While the dough is resting, place the almonds in a food processor and pulse a few times until finely ground. Transfer the almonds to a bowl and add the sugar, ground cinnamon, crushed mastic gum, almond extract, egg white, and orange blossom water. Mix well until all the ingredients are thoroughly combined.
Roll out the almond filling: On a flat surface, roll out the almond filling between two sheets of waxed paper into a rectangle measuring 30 x 22 cm (12 x 7 inches).
Roll out the dough: Once the dough has doubled in size, roll it out between two sheets of waxed paper into a rectangle of the same size, approximately 30 x 22 cm (12 x 7 inches).
Layer the filling: Peel off the top sheet of waxed paper from both the dough and the almond filling. Carefully invert the almond filling onto the dough, aligning the edges.
Shape the cookies: Using a pizza cutter, cut the layered dough into three equal portions. Starting from the long side of each portion, roll it up tightly, jelly-roll style, to form three equal logs. Wrap each log in plastic wrap and roll it back and forth several times to smooth it out. Gently flatten each log with your fingers to reduce its thickness.
Cut the cookies: Using a pizza cutter, slice each log into equal diamond-shaped pieces, approximately 2.5 cm (1 inch) wide.
Arrange and decorate: Transfer the cookies to a baking sheet lined with parchment paper. Use the tines of a fork to make crisscross marks on each cookie, then brush the tops with the beaten egg.
Bake the cookies: Bake in a preheated oven at 200°C (400°F) for about 12 minutes, or until the cookies turn golden. Let them cool slightly, then enjoy!