Combine the first 5 ingredients in a medium bowl. Use an immersion blender to create a smooth sauce with some texture. A standard blender can work, but the sauce should have about 3 cups of sauce. Chill in the refrigerator for at least 4 hours.
In a large pot, bring 3 quarts of water, the crab boil, and salt to a boil. Add shrimp. When the water starts boiling again, turn off the heat, cover, and let the shrimp sit for 5 minutes to absorb the seasonings.
Drain shrimp and cool. A bowl of ice works well for this. Peel them and, if desired, remove the dark vein along the back of the shrimp.
Place shrimp in a bowl, add sauce, and gently toss to coat. To serve, create mounds of lettuce on 6 dessert plates. Arrange 6 shrimp on each plate and top the shrimp with a tablespoon or so of chopped egg. If desired, garnish with a little chopped green onion and parsley.
