Preheat the oven to 500 degrees F.
Heat the butter, olive oil and garlic in a very large ovenproof saute pan over medium-high heat until hot. You may need two pans for this. Add the crab, season to taste with salt and pepper and toss well.
Transfer to the oven and roast until the garlic turns light brown and the crab is heated through (about 12 minutes). Toss once halfway through. Pour the contents of the pan into a large warm serving bowl, add the lemon juice and the parsley and toss well.