Boil 8 quarts of water with 3 tablespoons of salt in pot. Add whole lobsters and cook for 8 minutes. Refresh pot in ice water for 10 minutes, or cool enough to handle. Remove lobster meat from tails and claws, and reserve until ready to serve later. Reserve the lobster stock.
To prepare stock, in another large stock pot add 2 tablespoons of neutral oil. Saute onion, garlic, carrots, celery and lemongrass for 2 minutes.
Add green curry paste, shrimp paste, fish sauce and lobster bodies and shells and stir until incorporated.
Add palm sugar and 8 quarts of water to the stock pot with the vegetables and lemongrass and bring to a boil. Reduce to simmer and cook for one hour.
Strain stock into a large heat-proof bowl, pressing the juices from the lobster shells. Return to stock pot, add the prepped Idaho sweet potato and boil until tender, about 10 minutes. Working in batches, slowly add stock to a blender or Vitamix taking care not to add too much at a time.
Wipe your stock pot clean and add a small amount of vegetable oil, quickly saute shiitake mushrooms. Add coconut milk, heavy cream, lobster stock and cubed sweet potato. Bring stew to a boil, reduce flame to simmer and cook for 30 minutes.
Adjust salt and pepper. Chop reserved lobster meat into bite sized pieces and add to stew briefly taking care not to overcook.
Garnish with finely chopped chives or cilantro - Serve immediately with oyster crackers or fresh corn tortilla chips.