1. Whisk lime juice, fish sauce, 2 tablespoons water, sugar, garlic, and jalapeño in medium bowl until sugar dissolves. Reserve 1 tablespoon in large bowl; toss carrots with remaining dressing and set aside.
2. Heat oil in 12-inch nonstick skillet over high heat until beginning to smoke; add asparagus and cook until browned and tender-crisp, about 4 minutes, stirring once every minute. Transfer to large plate and place in freezer 5 minutes.
3. Toss watercress with reserved 1 tablespoon dressing and divide among salad plates. Toss asparagus and mint with carrot mixture and place a portion over watercress; sprinkle salads with peanuts and serve.
STEP BY STEP: Cutting Asparagus on the Bias
1. To cut the asparagus quickly and evenly, arrange the spears in staggered groups of five on a cutting board.
2. Cut them into 1-inch pieces on the bias.