Put noodles in a large bowl and cover with just-boiling water. Let noodles sit until tender, 5 to 8 minutes.
Meanwhile, cut cucumber and carrot into 4-in. lengths and then into matchsticks, using a mandoline* or other hand-held slicer, to yield 1/2 cup matchsticks of each (or cut cucumber into matchsticks with a knife and coarsely shred carrots).
Drain noodles and rinse with cold water. Spread noodles out on a baking sheet lined with a kitchen towel. Pat dry.
Divide noodles into 2 long "logs," then cut with scissors to total 10 equal portions.
Set out all ingredients except the sesame sauce near a work surface. Pour very hot tap water into a large shallow bowl such as a pie plate. Submerge 1 rice-paper wrapper until moistened and softened slightly but not completely pliable (it will continue to soften as you work with it).
Lay wrapper on work surface and put 1/2 lettuce leaf in center. Mound 1 portion of noodles on lettuce followed by about one-tenth of the cucumber, carrot, and apple slices; 3 mint leaves; 4 cilantro leaves; and a sprinkling of onions. Arrange ingredients into a rectangle about 4 in. long. Fold paper over short ends of filling, then roll up tightly from a long side. Repeat to make remaining rolls. Serve with sesame sauce.