To prepare the curried crabmeat, heat a 2.5-qt. saucepan over medium-high heat. When the rim of the pan is hot-to-the-touch, add the sesame oil, shallots, ginger and garlic. Cook for 2 - 3 minutes, until lightly caramelized (golden brown and aromatic).
Add carrot and pepper and continue cooking for 1 - 2 minutes. Add curry paste and turmeric. Cook and stir an additional minute, until well blended and fragrant.
Lower heat and stir in the yogurt. Bring this mixture barely to a boil and add the crabmeat. Stir in cilantro. Season with salt and pepper and transfer to a fondue pot.
To serve, skewer a chunk of lobster on a fondue fork and dunk it into the curried crab sauce.