Heat oven to 375°F (convection) or 400°F (conventional). Line 6 half sheet pans (18"x13") with parchment paper. Coat parchment in each pan with cooking spray. Have 6 more pans and sheets of parchment paper prepared.
Slice potatoes 1/16-inch thick with a mandolin, and immediately immerse them into a bowl of cold water. (Sliced potatoes can be refrigerated in water about 2 hours.)
Working with 12-14 ounces of sliced potatoes at a time, spin dry in a salad spinner or pat dry between towels.
Evenly sprinkle one prepared pan with 1/4 cup Parmesan. Arrange 12-14 ounces of sliced potatoes over Parmesan, in a thin even layer covering pan without any spaces between the potatoes. Sprinkle top with 1/4 cup Parmesan. Spray evenly with vegetable spray. Place second sheet of parchment and another pan on top. Repeat 5 more times with remaining potatoes.
Bake 25-30 minutes until potatoes are just barely browned on edges and cooked through. (Check by lifting pan and parchment.) Remove from oven and cool completely with pan on top. Carefully remove top layer of parchment paper.
With sharp scissors, cut sheet of potatoes into 4 even rectangles, approximately 5x7-inches each, cutting through the potatoes and bottom parchment.
Toss herbs and green onion together in a bowl. Mise en place the herbs, cucumber, red pepper, carrots and shrimp.
Arrange filling crosswise on potatoes, using several strips of cucumber, red pepper, carrots, about 1 tablespoon herbs, 3-4 shrimp and one teaspoon peanuts if desired. Roll starting on the short edge, holding paper from underneath as you roll. Repeat with remaining potatoes and filling. Cut diagonally crosswise.
Serve with side of slaw and Hoisin or peanut sauce for dipping. Okay to prepare up to 2 hours ahead.