How to Make It
Process shallots, 1/4 cup oil, 2 tablespoons water, ginger, chile, and garlic in a blender until almost smooth, about 20 seconds.
Heat a medium skillet over medium. Add shallot mixture and lime leaves. Cook, stirring constantly, until lightly browned, about 5 minutes. Stir in brown sugar, tamarind puree, and remaining 1 cup water. Bring to a boil; stir in flaked coconut and 1/2 teaspoon salt. Return to a boil; reduce heat to low. Cook, stirring often, until mixture is almost dry, about 10 minutes. Remove from heat.
Bring a large pot of salted water to a boil over medium-high. Add green beans; cook 2 minutes. Add cabbage, broccoli, and bok choy; cook until vegetables are just tender, about 45 seconds. Using a slotted spoon, transfer vegetables to a large colander, and immediately rinse under cold running water; drain well.
Add cellophane noodles to water in pot; cook over medium-high until noodles are completely translucent, about 2 minutes. Drain and rinse under cold running water; drain well.
Place drained vegetables in a large bowl; add noodles, coconut mixture, remaining 1 tablespoon olive oil, and remaining 11/2 teaspoons salt. Gently toss to combine, making sure coconut mixture is evenly distributed. Garnish with scallions, cilantro, and toasted coconut.
Find tamarind puree, makrut lime leaves, and cellophane noodles at Asian markets or on amazon.com.