Start coals in grill or preheat broiler.
In a saucepan, melt butter over medium heat until foamy.
Add shallots and saute until pale golden, about 4 minutes.
Squeeze in lemon juice, a slice at a time, until sauce is tangy but not overwhelmingly acid.
Keep sauce warm over lowest possible heat.
Place crab on grill or under broiler, cut side up, and cook for 10 to 12 minutes (cooked crab) or up to 20 minutes (raw crab).
Baste several times by tipping a teaspoon of sauce into shell through the cross.
When done, the crab meat will be opaque and slightly firm, and the underside of the shell will be well browned.
Cut crab in two (use scissors or shears) and pass any remaining sauce and the lemon wedges.