Step 1

Working in batches, toss together wings and starch in a large bowl to coat, shaking off excess. Repeat process, working in batches, to coat all wings a second time. Place in an even layer on wire rack set inside a large rimmed baking sheet. Let stand at room temperature until starch begins to appear wet, about 15 minutes.

Step 2

Heat 3 ½ cups oil in a large high-sided pan over medium-high until a deep-fry thermometer registers 350°F, adjusting heat as needed to maintain temperature. Working in batches, fry wings, turning often, until light golden brown, 3 to 4 minutes. Drain on a baking sheet lined with paper towels. Working in batches, return fried wings to hot oil; fry, turning often, until golden brown, about 2 minutes. Return to baking sheet.

Step 3

Combine jalapeños, brown sugar, soy sauce, garlic, and remaining ½ cup oil in a medium skillet. Cook over medium-high, stirring occasionally, until oil begins to bubble, about 2 minutes. Place 5 wings in sauce in skillet; toss constantly using tongs until wings are deep golden brown and fully coated, about 30 seconds. Place wings on a serving platter. Quickly repeat process with remaining wings. Garnish with additional fresh jalapeño slices and, if using, chrysanthemum greens.