Preheat oven to 375°F.
Melt 3 tablespoons butter in a sauté pan over medium heat. Add celery, shallots, garlic, thyme, and salt and pepper and sauté to tender, 5 minutes or so. Deglaze the pan with sherry, vermouth or wine. Remove from heat.
Season crab with lemon juice, Tabasco and 1 tablespoon Old Bay.
Make the base sauce for the mac: Bring cream, garlic and mustard to a low boil and simmer 5 minutes to thicken. Remove garlic clove and add in cheese; stir to melt.
Combine cracker crumbs, remaining tablespoon Old Bay and Parm in a bowl. Melt remaining 3 tablespoons butter, then pour over crumbs; stir to coat.
Combine pasta, base sauce, shallot mixture and crab then pour everything into a casserole dish. Top with cracker crumb mixture and bake until brown and bubbly. Garnish with chives and parsley to serve.