Heat a large pot of water over high heat and let it come to a boil.
Slice the hardy bottom 2 inches off the base of the napa cabbage leaves and discard. Boil the leaves in the water for 2 and a half minutes until soft and pliable.
Remove the leaves from the pot and set aside to cool.
While the leaves are cooling, place carrot, green onions, garlic, and ginger in a food processor, and process until they are chopped into small pieces.
Add shrimp, sesame oil, tamari, salt, and pepper, and pulse until chopped and combined. If you don't have a food processor, you can chop everything into small pieces with a sharp knife and mix together in a bowl.
Use the napa cabbage leaves to roll up the filling: Place a leaf flat on a plate or a cutting board then add about 3 tbsp of the filling at the base of the cabbage. Roll the cabbage to encase the filling. You can fold up the sides to close them up but it's not necessary.
Once all the cabbage rolls are made, heat 1 tbsp of avocado oil in a large skillet over medium high heat.
Once hot, add cabbage rolls in a single layer. You'll work in 2-3 batches. Cook for 3 minutes, flip then cook for another 3 minutes until the filling is cooked through and the leaves are browned. Repeat with the remaining avocado oil and cabbage rolls.
Combine all ingredients for the dipping sauce in a small bowl.
Garnish with toasted sesame seeds, and enjoy warm with dipping sauce.
