1. In a bowl, place the aniseed and pour 1 cup of hot water over it. Set aside for 5 minutes and then strain. In another bowl, combine the yeast, sugar, and 1 cup of lukewarm water. Stir until the yeast dissolves. Set aside for 5 minutes to activate.
2. In a large bowl, sift the flour and add the salt, mastic, and mahlab. Mix well. Pour in the olive oil and 'ryziase' (rub the mixture between your palms) until coarse crumbs form. Add the yeast mixture and gradually add the strained aniseed tea.
3. Knead well and shape the dough into a ball. Cover the bowl with a towel and leave the dough in a warm place for about 1–2 hours until it doubles in size. Place the sesame seeds in a bowl and pour hot water over them. Set aside for 5 minutes and then strain. Place the dough on your work surface and knead for 2-3 minutes. Divide it into 4 portions.
4. Take each portion one by one and shape it into a small ball. Roll it out with a rolling pin into an oval shape. Line 2 baking trays with parchment paper and place the Laganes (flatbreads) on them. Brush them lightly with water and sprinkle with some sesame seeds, pressing gently so they stick well to the Laganes. Wet your fingers and make deep indentations all over their surface.
5. Cover the trays with a kitchen towel and let the Laganes rise in a warm place for 40-60 minutes. Bake in a preheated oven at 180°C (350°F) for 20 minutes, or a little longer if you prefer them crispier. Place the Laganes on a rack to cool and serve with a dip of your choice, such as hummus or taramosalata.