Crack the crab reserving the juices and tomalley. Set aside.
Make the tomalley sauce by pushing the tomalley through a sieve with a wooden spoon into a small pot. Add the chili flakes, thyme, garlic, and lemon juice. Mix in the reserved crab juices and bring to a quick simmer over low heat. Give it a final quick stir and remove the pan from the heat. Pour the tomalley mixture into a small mixing bowl and allow it to cool. (Start roasting the crab once the tomalley sauce is cooling.) As soon as the tomalley sauce feels lukewarm to the touch, add the mayonnaise or aioli along with the salt and pepper. Taste and add more salt, pepper, or thyme, if you like.
Put a rack in the middle or lower third of the oven and preheat the oven to 500 degrees F.
On the stove, in a large oven-proof saute pan or casserole, heat the butter, olive oil, garlic, thyme, and lemon zest over medium-high heat until hot. Add crab pieces and season with salt, pepper, to taste, and mix well. Put the pan in the oven and cook until the crab is hot throughout and the garlic is golden brown. (Watch carefully; the crab heats very quickly and at 500 degrees F the garlic can burn easily.) Remove the crab from the oven, drizzle with 4 tablespoons of lemon juice and scatter the parsley over the top.
To serve, stack the crab on a platter and drizzle with the tomalley sauce or serve the tomalley sauce in a small bowl and allow your guests to help themselves. Garnish the platter with lemon wedges and slices of garlic-rubbed toast. Serve immediately.
Recipe courtesy of Cat Cora