How to Make It
In a small bowl, whisk the light brown sugar with the lime juice, fish sauce, chiles and garlic until the sugar is dissolved.
Cut half of the kale into thin ribbons and transfer them to a large bowl. Cut the rest of the kale into 4-inch wide pieces. Trim the brussels sprouts, reserving 2 loose cups of the whole outer leaves. Thinly slice the remaining brussels sprouts and add them to to the kale ribbons in the bowl along with the basil, scallions, cilantro and mint.
In a large skillet, heat 1/2 inch of vegetable oil until shimmering. Line a large baking sheet with paper towels. Add the brussels sprout leaves to the skillet and fry over moderately high heat, turning occasionally, until browned in spots, about 2 minutes. Using a slotted spoon, transfer the leaves to the paper towels to drain. Working in batches, add the large pieces of kale to the hot oil and fry until translucent and crisp, about 3 minutes per batch. Drain on the paper towels. Add the dressing, crispy brussels sprouts and kale to the salad and toss to combine. Serve right away.