Lightly toast the Sesame Seeds in a dry skillet over medium heat until fragrant and golden; set aside to cool.
Steep the Saffron Threads in a few tablespoons of warm Water to release their color and aroma.
In a large bowl combine the All-Purpose Flour with Baking Powder, Instant Yeast, Ground Anise, Ground Fennel Seeds, Ground Cinnamon, Ground Turmeric, Ground Mastic and Salt; whisk briefly so the spices are evenly distributed.
In a separate bowl beat together the Egg with Olive Oil, melted Unsalted Butter, a splash of White Vinegar and a tablespoon or two of Orange Blossom Water, then stir in the saffron-infused water.
Make a well in the dry ingredients and pour in the wet mixture. Mix and knead, adding extra Water a little at a time, until you have a smooth, pliable dough. Cover and let it rest for about 30–45 minutes to relax and allow a slight rise.
Divide the dough into portions, roll each portion very thin, and cut into long strips. Fold and pinch each strip into the traditional chebakia flower shape (four or five loops pinched in the center) and press the center firmly so they hold during frying.
Heat enough Neutral Oil in a deep pot to deep-fry the pastries. Fry the shaped chebakia in batches over medium-high heat until deep golden and crisp, turning once so they color evenly. Drain on paper towels.
Warm the Honey gently in a saucepan just until it loosens; stir in a little extra Orange Blossom Water to flavor and, if you like, a small knob of Unsalted Butter to give the glaze a silky shine.
While the honey is still warm, dip each fried chebakia into it, letting excess drip back into the pan, then toss or sprinkle with the toasted Sesame Seeds and some chopped or ground Almonds for texture.
Arrange the glazed chebakia on a rack to cool and let the honey set slightly; they will be crisp, sticky and fragrant—best enjoyed within a few days stored in an airtight container.
