Step 1Combine the sour cream, garlic, tarragon, mustard and salt. Cover and let the sauce stand.
Step 2Remove crab meat from the leg and cut it up into bite-size pieces. Cover the meat and set it aside.
Step 3Trim the tops and stems of the artichokes. Stand the artichokes upright in the top of steamer and steam them until a leaf easily pulls out of the artichoke, about 45 minutes. Remove the artichokes from the steamer. When they're cool enough to handle, remove the leaves and discard them, then scoop out the chokes with a spoon. Cover the artichoke bottoms until serving.
Step 4Heat the butter in a nonstick skillet over medium heat until melted. Add the shallot and cook lightly, about 1 minute. Stir in the crab meat and cook it until the crab is hot through, 1 to 2 minutes. Pour the eggs over the crab meat. Let the eggs begin to set around the edges and gently stir until eggs are set.
Step 5Place an artichoke bottom on each plate and spoon over each the cooked crab, eggs and a dollop of the tarragon cream.