- 1/4 cup sesame seeds, toasted
- 1 1/3 lb shrimp, shelled and deveined
- 3 scallions, chopped
- 1 tablespoon Asian sesame oil
- 1 tablespoon soy sauce
- 1 tablespoon cornstarch
- 1 1/2 teaspoons minced peeled fresh ginger
- 1 teaspoon minced garlic
- 12 (17- by 12-inch) phyllo sheets, thawed if frozen
- 1 1/4 sticks (1/2 cup plus 2 tablespoons) unsalted butter, melted
- 1 large egg, lightly beaten
- 2 tablespoons sesame seeds, toasted
- Kosher salt for sprinkling
- Accompaniment: apricot dipping sauce
- Pulse together all filling ingredients in a food processor until they form a coarse paste.
- Preheat oven to 450°F.
- Cover phyllo with 2 overlapping sheets of plastic wrap and then a dampened kitchen towel. Put 1 phyllo sheet on a work surface, keeping remainder covered, and brush generously with butter. Stack 2 more phyllo sheets on top, generously buttering each.
- Cut phyllo stack in half lengthwise, then arrange 1 half with a long side nearest you. With dampened fingers shape 3 tablespoons shrimp filling into a narrow rope along edge nearest you, then roll up paste tightly in phyllo to form a long thin roll. Make another roll with other half of stack. Make 6 more rolls with remaining phyllo sheets, butter, and shrimp filling.
- Lightly brush top of rolls with egg and sprinkle with sesame seeds and kosher salt. Cut each roll crosswise into 4 sticks and arrange, seam sides down, 1 inch apart on 2 large baking sheets. Bake sticks in upper and lower thirds of oven, switching position of sheets halfway through baking, until phyllo is golden brown, about 15 minutes total.
- Transfer sticks to a rack to cool slightly and serve warm with dipping sauce.