Bring a large pot of lightly salted water to a boil. Add bouquet garni, crab boil, lemons, halved garlic, corn, and sausage. Add blue crabs and cover. Cook for 10 minutes or until crab is cooked through.
In a small saute pan over medium heat, melt butter with the 3 peeled garlic cloves. Simmer the butter for 3 to 4 minutes. Remove from the heat and discard the garlic cloves.
Remove the crabs, corn, and sausage from the crab boil and serve on newspaper, with butter sauce over top.