Ready in 1 hour
Sweet, salty, and spicy, nuoc cham is the indispensable sauce of Vietnam's cuisine. It's a favorite dipping sauce for spring rolls and for fresh rice-paper rolls such as these
Whisk all ingredients in medium bowl until sugar dissolves. Let stand at least 30 minutes. DO AHEAD Can be made 1 day ahead. Cover; chill.
Heat oil in medium skillet over medium-high heat. Add mushrooms and sauté until soft, about 5 minutes. Cool.
Place rice sticks in large bowl; add enough hot water to cover. Let stand until softened, about 30 minutes. Drain. Cut into 6-inch lengths; set aside. Fill same bowl with warm water. Add 1 rice-paper sheet and turn until beginning to soften, about 30 seconds (sheet will still be stiff in a few spots). Remove from water; drain on kitchen towel. Repeat with 5 more rice-paper sheets, arranging in single layer.
Divide half of mint, cilantro, and basil among softened rice-paper sheets, arranging in line across lower third of each sheet and leaving 1-inch border on each end. Top with half of rice sticks, shaping into compact log. Top with half of lettuce, sprouts, cucumber, carrot, shrimp, and mushrooms. Fold bottom of each rice sheet over filling, then fold in ends and roll into tight cylinder. Place rolls, seam side down, on platter. Repeat soaking with remaining rice-paper sheets, then top with remaining filling to form 6 more rolls. DO AHEAD Can be made 6 hours ahead. Cover with damp paper towel and plastic wrap; chill.
Cut each roll diagonally into thirds. Arrange on platter and serve with sauce