1 1/2 tablespoons (packed) palm sugar or light brown sugar
1/4 cup fresh lime juice
3 tablespoons fish sauce (such as nam pla or nuoc nam)
1 teaspoon minced garlic
1/2 red Thai chile or 1/4 red jalapeño, seeded, thinly sliced
24 small Tuscan kale leaves (about 5 inches) or 5-inch-long pieces torn from large stemmed leaves
1 tablespoon vegetable oil
Kosher salt and freshly ground black pepper
3 cups (loosely packed) mixed tender herbs (such as cilantro, mint, and basil)
3 cups mixed shaved vegetables (such as carrots, beets, and radishes)
2 cups pea tendrils, watercress, or baby arugula
2 cups thinly sliced stemmed Tuscan kale leaves (from 1 bunch)
1 cup thinly sliced cucumber
Microwave sugar and 2 Tbsp. water on high in a medium microwave-safe bowl until sugar is dissolved, about 30 seconds. Let cool. Whisk in next 4 ingredients for dressing. Set aside.
Arrange racks in upper and lower thirds of oven; preheat to 250°. Brush tops of kale leaves with oil; season with salt and pepper. Arrange in a single layer on 2 large baking sheets. Bake, rotating sheets top to bottom halfway through, until kale is crisp, about 30 minutes. Transfer leaves from baking sheets to a wire rack; let cool.
Mix herbs and remaining 4 ingredients with 6 Tbsp. dressing in a large bowl. Divide salad among plates; top with crispy kale leaves and drizzle remaining dressing over.