Grind together toasted sesame seeds and almonds into a fine mixture.
Heat some water in a microwave for 10 seconds. Remove from heat, add yeast and sugar. Mix well and set aside till the yeast activates.
Combine flour, salt, cinnamon powder, star anise powder and baking powder in a bowl and mix well. Add ground mixture and mix well.
Add olive oil, vegetable oil, yeast, vinegar, ¼ teaspoon rose essence and butter, mix and knead into a soft and elastic dough.
Divide the dough into equal portions, roll them to flatten and cut into strips. Twist them.
Heat sufficient oil in a pan. Deep-fry the chebakia till golden and crisp. Drain on absorbent paper.
Heat honey in a non-stick pan.
Take saffron in a bowl. Add some water, mix and add to the honey along with the remaining rose essence. Mix well and let it warm a little.
Put the chebakia into the honey syrup and let them soak for a while.
Sprinkle toasted sesame seeds and black sesame seeds on top and serve.