Make tahini drizzle: Combine lemon juice, miso paste, tahini, dates, garlic, and red pepper flakes in a blender. Blend, adding water 1 tsp. at a time, until mixture reaches desired consistency.
Make wraps: Place nori sheets on a flat surface. Divide cabbage, carrot, squash, cucumber, and avocado among sheets. Top each pile with 1 heaping Tbsp. Spicy Tahini Drizzle, then roll each sheet into a tube shape.