Shred carrot and apple with a cheese grater. Steam edamame according to package directions or until heated through (usually about 3- 4 minutes in the microwave). Peel cucumber and slice into rounds.

Lay out tortillas; spread cream cheese onto each, and layer with ham, carrots, and apples. Roll up tightly and slice crosswise into "sushi rolls."

Serve with edamame and sliced cucumbers on the side.