Heat the oven to 425 F.
In a medium mixing bowl, whisk together the eggs, mayonnaise, mustard, ¾ teaspoon Old Bay Seasoning, tarragon, onion and celery to make a dressing.
In a large mixing bowl, toss the bread with half of the dressing, mixing until the dressing is absorbed by the bread and the cubes are slightly broken up. Add additional dressing if the cubes are too dry.
Gently mix in the crab, being careful not to break up the lump pieces. The mixture should hold its shape when formed into a ball with your hand. If it is too dry, add additional dressing until the mixture comes together. You might not use all the dressing.
Divide the mixture and form into 16 mini crab cakes (or 8 full-size crab cakes). Place the cakes on a greased cookie sheet or sheet pan.
In a small bowl, stir the butter together with the remaining one-half teaspoon Old Bay Seasoning. Top each cake with a small dollop of the seasoned butter.
To make the dipping sauce: stir together the mayonnaise, mustard powder, salt, Worcestershire sauce, Dijon mustard and heavy cream.
Serve the crab cakes with sauce, parsley and lemon wedges.