Wash taro and potatoes then boil or steam until barely fork tender, about 12 to 15 minutes; cool immediately.
In a small frying pan over medium high heat, saute onions with 2 tbsp. of olive oil for 5 to 10 minutes, until caramelized.
In the meantime, grate the taro, potatoes and parmesan cheese into a large mixing bowl. Then add the crab meat, ¼ cup green onions, ¼ cup parsley, salt, pepper to taste and eggs to the mix and stir lightly.
Once onions are slightly browned, remove from heat and set aside to cool for 4 to 5 minutes.
Add ¼ cup lemon juice, panko and cooled onions to the crab meat mixture; lightly fold all ingredients together until evenly mixed.
Heat 1 tbsp. olive oil in a sauté pan over medium high heat. Once oil is hot, place 1 scoop or a 3 oz. portioned patty of the crab mixture into the pan and lightly press the top with a spatula, to form a rustic style cake. Place a few more patties in the oil, being careful not to over crowd pan or splash oil. Cook both sides until they reach a golden caramelized color.
To make the garlic aioli, mix the mayonnaise, garlic, ¼ cup parsley, ¼ cup green onions, basil, lemon zest and ¼ cup juice in a large mixing bowl. Fold in sour cream, then season to taste with salt and pepper. Set aside, and keep chilled until ready to serve.
Serve crab cakes warm, with a dollop of garlic aioli.