Slice bell pepper and cabbage into wisps and coarsely shred carrot on a box grater. Slice avocado thinly lengthwise. Rinse sprouts and roll them up in a clean kitchen towel to dry.
Thinly spread lavash with hummus, spreading almost but not quite to the edges. Arrange each vegetable in adjoining rows.
Tightly but carefully, roll up each lavash, sealing end with a bit of extra hummus if it’s springing open, and roll over onto the seam. Cut into 1 1/2-in.-thick pinwheels, then chill.
MAKE AHEAD Up to 1 day, chilled.