Step 1 Place the crab in a large pot and cover with water. Place the pot over high heat and bring to a boil. Cook for 15 minutes. Drain the crab and rinse under cold running water. Refrigerate until almost ready to serve, about 1 hour.
Step 2 About 30 minutes before serving, heat the oven to 350 degrees and remove the crab from the refrigerator. Pull off the legs and claws. Crack the large sections of each using the back of a heavy knife or a nutcracker. Arrange on a platter. Lift off the top shell. Using a small spoon, scoop out all of the golden butter and any ivory fat. Set these aside in a small bowl. With your fingers, pull away the slender, finger-like gills and discard them. Also pull away the thin, hard jaws from the front of the crab and the fat "spade" from the bottom. Using a heavy chef's knife, cut the body in half lengthwise, then in half again crosswise, cutting through the leg joints to expose as much meat as possible. Add these to the platter.
Step 3Spoon the crab butter and the fat into a strainer and using the back of a wooden spoon or a plastic spatula, press them through the strainer into another bowl. (Be sure to scrape the bottom of the strainer; much of the crab butter collects there.) You should get about one-quarter cup of strained crab butter. Add the mayonnaise, vinegar and salt and whisk until smooth. The mixture should be about the consistency of stirred yogurt. Taste the mixture; it should be intensely crabby and slightly sharp. If necessary, squeeze in a little lemon juice. Arrange the baguette slices on a baking sheet and spoon 2 to 3 teaspoons of this crab mixture onto the center of each baguette slice. Bake until the crab mixture is puffed and golden and the edges of the baguette are beginning to brown, 10 to 12 minutes.
Step 4Arrange these crab toasts on the platter around the crab pieces or on a separate platter. Careful, they're hot. Serve immediately.