Preheat your oven to 375 degrees F.
Place the crab legs, white wine, and lemons into your baking dish or a rimmed baking sheet. Cover the dish with aluminum foil and place into your preheated oven on the middle rack.
Bake the crab legs for 15 minutes, or until the king crab shells are hot to the touch.
Remove from the oven and serve hot with the creamy butter sauce.
Make the Garlic Butter Sauce
In a medium sized saucepan, melt one tablespoon of butter over medium heat with the wine, grated shallots, grated garlic, fresh thyme, and lemon zest. Sauté for 1 to 2 minutes, it should be very fragrant.
Whisk in the chicken broth and lemon juice, let the mixture reduce down until there's about 3 tablespoons of liquid remaining.
Add the cream and turn the heat up to medium-high. Bring to a boil, then turn the heat down to low.
Whisking constantly, add the rest of the cold butter ONE tablespoon at a time, whisking until each one is incorporated completely before adding the next one.
Continue adding in all the butter, by the time the last tablespoon is done the sauce should be creamy and coat the back of a spoon.
Let sit at low heat, stirring occasionally, until ready to serve with the crab legs.