What is the best way to cook lobster claws?
Get a pot of seawater to a good simmer and put that claw in till internal temp is 160, then ice it to stop the cook . If not seawater than any water to the saltiness like seawater. Depending on size of claw, I'm not sure how big you got, we had anywhere from 1lb to 23lb lobsters at the shop I worked last year , that's anywhere from 2oz claw to 8lbs for one claw....obviously way different cook times, use a probe thermometer cuz over cooked is worse than beyond a well done piece of leather and any less than perfect is blue/green/black snot. The 23lb lobster sat in the boiler for 1.5hrs , it had an 8lb claw but that timeframe was mostly due to the enormous body on the damn thing. Xl lobsters really require the low controlled simmer or the tips of the claws go to rubber, almost impossible to prevent when they get over 10lbs. But since you are asking about one single claw that is "?" Weight , using a thermometer will be key.
Shout out to Alma Lobster Shop, a fine group of folks , I had a great summer.
Steam it for maybe 5-8 minutes in a steamer. Failing this you can boil it for maybe 6 minutes or. It is very important not to overcook lobster otherwise it becomes tough. Dungeness crab is a lot more forgiving in that regard (an extra 10 minutes of steaming/boiling will make not much of a difference).