Prepare a grill to medium-high heat.
In a large roasting pan over high heat, add the stock, mirin, soy sauce, ginger, toasted sesame oil and lime juice and bring to a boil. Add the crabs, shell-side up, and place the pan on the grill. Cover the grill and steam the crabs until they are just cooked through, about 30 minutes, flipping the crabs halfway through cooking. Remove the crabs to a platter.
Strain the steaming liquid into a bowl. Return the liquid to the roasting pan and whisk in the honey, black pepper and chile flakes. Bring to a boil and simmer until slightly reduced, about 10 minutes. Whisk in the butter. Halve the crabs and put 2 halves into 4 serving bowls. Pour the sauce over and garnish with cilantro.