Whisk together mayonnaise, scallions, eggs, mustard, Old Bay (you can find it at any major grocery store), and lime juice. Fold in the crab, followed by 1 1/2 cups panko, sesame seeds, and salt and pepper to taste. Divide into 8 equal portions, and form into patties. Refrigerate for 10 minutes.
While the crab cakes are chilling, prepare the tartar sauce by stirring together all the ingredients in a medium bowl. In a non-stick or cast iron skillet, heat 3 tablespoons oil over medium heat. Dredge the crab cakes in the remaining 1/2 cup of panko and fry until golden brown, 3-4 minutes per side. Serve with tartar sauce and lime wedges.