Heat a small non-stick frying pan over medium-high heat and toast the sesame for about 3 minutes, or until golden in colour and start to pop, stirring constantly. Be careful, seeds can easily burn. Remove to a plate immediately.
For the dough: Mix the dry ingredients in a large mixing bowl. Gradually add the water and mix well with your hands. The dough will be soft and sticky. Gather the dough and coat with 1 tablespoon sunflower oil. Cover with plastic wrap and let rest in a warm place for at least 2 hours.
Frying the zalebiya: Heat the oil in a large heavy-bottomed pan over medium-high until it reaches 180 °C, 350°F on a deep-fry thermometer (see tip below). While the oil heats, line a tray with a double layer paper towels for draining the zalebiya. Have on the side a cup half-filled with oil to grease your fingertips.
Working in batches of 3 or 4, shape the dough and immediately fry as follows keeping in mind that the pace of work should be coordinated and fast:
Shaping the dough: With your hand take one portion of dough about 5 cm. Poke two holes (or three holes) in the ball with your index fingers and thumbs and carefully stretch the dough into an oblong shape about 15 cm.
Frying the dough: Have at hand 2 spoons (for the holes) and 2 forks (to turn the dough in the oil and remove to the plate). Carefully lower one end of a Zalebiyah into the hot oil, and immediately stick the handle of a spoon into the first hole, and almost at the same time, lower the other end and stick the handle of another spoon in the second and third holes and stretch. This should take one to two seconds. Fry until golden brown on the underside for about 2 to 3 minutes. Carefully turn the zalebiyah over and fry for an additional 2 to 3 minutes, or until golden brown as well. Remove the zalebiyah to the paper towel-lined tray.
Serve at room temperature. Tastes best when freshly made.