Finely shred the cabbage and carrots in a food processor or by hand. Place carrots and cabbage in a small mixing bowl. Add black & tan sesame seeds. Mix in lime juice and set aside.
In a medium frying pan melt coconut oil over medium high heat - add re-hydrated mushrooms and saute until crispy and golden brown. Remove from heat and set aside.
Fill a pie plate or casserole dish (large enough to completely emerge your rice paper spring roll paper) with hot water. Set up your wrapping station: Make sure to have your mushrooms, filling and alfalfa sprouts within arms reach.
Working with one spring roll wrapper at a time, submerge rice paper round into the warm water until it softens, transfer the round to the work surface. Place 2 tablespoons of the carrot/cabbage mix, a few alfalfa sprouts and 2-3 slices of mushrooms on the wrapper and roll up the spring roll.
To make the peanut dipping sauce: whisk all the ingredients in a mixing bowl until completely unified.