Preheat the oven to 200°C (400°F).
First, clarify the butter (if you are using store-bought ghee, skip this step). In a small saucepan, melt the butter over medium-low heat. Skim off any white foam that rises to the top. Transfer the melted butter to a small glass container and let it sit for about 10 minutes. Once the milk solids have completely settled to the bottom, carefully pour the clear, golden liquid into a separate bowl, leaving the white solids behind. Discard the solids.
In a large bowl, combine the flour, salt, your prepared clarified butter, sunflower oil, sugar, the lightly beaten egg, anise seeds, mahlab, vanilla extract, baking soda, and water. Knead the mixture just until you obtain a soft, cohesive, and slightly sticky dough.
Divide the dough into equal portions, shaping them into balls roughly the size of a ping-pong ball (or slightly smaller). From here, you can shape your kaak in one of two ways:
For traditional ring-shaped kaak: Roll a dough ball between your palms to form an elongated rope about 7 cm (2.5 inches) long. Pinch the two ends of the rope firmly together to form a clean circle. I prefer my kaak nice and round!
For log-shaped kaak: Simply roll the ball between your palms until it forms a straight, elongated rope about 7 cm (2.5 inches) long.
Dip each shaped piece of kaak into the sesame seeds, pressing gently to ensure both sides are evenly coated. Arrange them on parchment-lined baking sheets, leaving a bit of space between each piece.
Bake for 20–25 minutes or until they turn a beautiful, pale golden brown. Keep a close eye on them toward the end, as every oven behaves a little differently!
Happy eating!