Preheat the oven to 325 degrees F. Line 2 baking sheets with parchment paper. Pulse the sugar and 2 tablespoons sesame seeds in a food processor until finely ground.
Transfer the ground sesame mixture to a medium saucepan and add the butter, orange zest and juice, cornstarch and salt. Cook, stirring occasionally, until the mixture comes to a simmer and thickens slightly, about 3 minutes. Transfer to a large bowl; stir in the flour, vanilla and the remaining 2 tablespoons sesame seeds. Refrigerate until cooled and thickened, about 45 minutes.
Drop heaping teaspoonfuls of batter, 4 inches apart, onto the prepared baking sheets. Lightly sprinkle the tops with more sesame seeds. Bake, 1 baking sheet at a time, until golden brown, about 10 minutes. Let cool on the baking sheet until just set enough to lift with a spatula, 1 to 2 minutes, then carefully transfer to a rack. While the cookies are still warm, curl up 2 sides of each cookie with your fingers, then let cool completely. Repeat with the remaining batter (reline the baking sheets between batches).