Toast and grind sesame seeds and almonds. Set aside.
In a large bowl, combine flour, ground almonds, ground sesame, anise, cinnamon, and salt.
Add the egg, melted butter, olive oil, orange blossom water, vinegar, and baking powder.
Dissolve yeast in a little warm water and add it to the mixture.
Gradually knead in warm water until you form a smooth, elastic dough. Cover and let rest for 1 hour.
Divide the dough and roll out into thin sheets. Cut into rectangles and make 4–5 slits inside each, then shape into the classic chebakia rose form.
Heat oil in a deep fryer or large pot. Fry the chebakia until golden brown.
Immediately dip hot chebakia into warm honey mixed with orange blossom water. Let soak for a few minutes.
Drain and sprinkle with toasted sesame seeds.
Let cool completely before storing in airtight containers.