Preheat the broiler with a rack positioned about 6 inches from the heat source.
Arrange the split crab claws or clusters on a sheet pan. Brush with the melted butter and season with salt and pepper.
Melt the 4 tablespoons of butter in a small saucepan over low heat. Add the shallot and garlic and cook for 2 minutes, until softened.
Whisk in the lemon juice and stock. Hold at a gentle, low simmer for 2 to 3 minutes, then remove the pan from the heat entirely.
Broil the crab for 5 to 7 minutes, watching closely, until the shell edges are charred and blistered.
While the crab broils, whisk the truffle oil and chives into the sauce, off the heat. Taste and adjust salt.
Spoon the warm truffle sauce over the charred crab, scatter extra chives on top, and serve immediately.