To prepare salad, combine 1/2 cup boiling water and mushrooms in a bowl; cover and let stand 30 minutes. Drain mushrooms in a colander over a bowl, reserving 2 tablespoons soaking liquid. Discard mushroom stems, and thinly slice mushroom caps. Cook spaghettini in boiling water 2 minutes, omitting salt and fat. Add carrot; cook 1 minute. Add asparagus; cook 1 minute. Add peas; cook 1 minute. Drain well. Add mushrooms to salad; toss well.
To prepare vinaigrette, place 2 tablespoons reserved mushroom soaking liquid, cilantro, and next 9 ingredients (cilantro through jalapeño) in a food processor; process until smooth.
Combine salad, vinaigrette, onions, and 2 tablespoons peanuts in a large bowl; toss well. Arrange 1 1/4 cups salad mixture on each of 4 plates. Top each serving with 2 tablespoons sprouts; sprinkle each with 1 1/2 teaspoons peanuts.