Whisk the lime juice, fish sauce, water, sugar, garlic, and jalapeño in a small bowl until the sugar dissolves. Reserve one tablespoon of this dressing in a large bowl. Add the carrots to the remaining dressing in the small bowl and let them sit to soften slightly.

Heat the oil in a large nonstick skillet over high heat until the oil is just starting to smoke. Add the asparagus and cook, stirring occasionally, until the stalks are browned and crisp-tender, about 4 minutes. Transfer the asparagus to a plate and place it in the freezer for 5 minutes to halt the cooking and chill the vegetable.

Add the watercress to the large bowl with the reserved tablespoon of dressing and toss to coat. Distribute the greens among individual salad plates. Toss the chilled asparagus and mint into the carrot mixture, then arrange this over the watercress. Sprinkle with peanuts and serve immediately while the asparagus is still cool and crisp.