Using the 1/8-inch julienne blade of a mandoline or other manual slicer, cut unpeeled apples into julienne strips. In a bowl toss apples with zest, juice, and sugar and drain in a colander 20 minutes.
Let spring roll wrappers stand in package at room temperature 5 minutes. Melt butter and in a small bowl with a fork lightly beat egg. Remove wrappers from package and carefully peel off 1 wrapper, covering remaining stack with a dampened kitchen towel to prevent drying.
On a work surface arrange wrapper with a corner pointing toward you and lightly brush with some butter, leaving top corner dry. Arrange 1/4 cup shredded apple on wrapper in a 6-inch long loose pile from left to right corners. Turn bottom corner up to cover filling and gently tighten roll, pressing it toward you. Fold right and left corners toward center and roll away from you as tightly as possible without tearing wrapper. Seal dry corner to spring roll with some egg and cover loosely with plastic wrap. Make 11 more spring rolls in the same manner. Spring rolls may be prepared up to this point 4 hours ahead and chilled, covered.
Preheat oven to 200 degrees.
In a 2-quart saucepan heat oil over modertae heat to 360 degrees on a deep-fat thermometer and fry spring rolls, 2 or 3 at a time, turning occasionally, 5 minutes, or until golden brown. (Make sure oil returns to 360 degrees between batches.) With tongs transfer spring rolls as fried to brown paper or paper towels to drain and keep warm on a baking sheet in middle of oven.
To serve, cut 2 spring rolls in half diagonally and arrange, pointed ends up, in a ramekin or small cup on a plate. Repeat with remaining spring rolls. Add a scoop of vanilla ice cream to the center of each ramekin or cup and drizzle with caramel sauce