In a bowl, place the anise and add 1 cup of hot water. Set aside for 5 minutes and strain.
In another bowl, place the yeast, sugar and 1 cup lukewarm water. Stir until the yeast dissolves. Set it aside for 5 minutes to rise.
In a large bowl, sift the flour and add the salt, mastic and mahleb. Stir.
Add the olive oil and rub with fingers until the flour absorbs the oil and they shape large crumbs (riziasma). Add the yeast mixture and then the anise tea little by little. Knead well and shape the dough into a ball. Cover the bowl with a towel and place the dough somewhere warm for about 1-2 hours for it to double in size.
Place the sesame seeds in a bowl and pour over the hot water. Set aside for 5 minutes and strain.
Place the dough on your workstation and knead for 2-3 minutes. Separate in 4 pieces. Take the pieces one by one and shape into balls. Open into an oval shape with a rolling pin. Place non-stick baking paper on the 2 oven pans and put the Laganas inside. Rub some water on them and sprinkle some sesame seeds. Press the seeds so they stick onto the surface well. Wet your fingers and press them deep on the surface to shape holes. Cover the pans with kitchen towel and place the Laganas somewhere warm for 40-60 minutes to rise.
Cook in a preheated oven at 180°C for 20 minutes or a bit more if you like them crispier. Place the Laganas on a rack to cool down and serve with a dip you like, such as hummus or tarama.