Gently mix the crabmeat, scallions, herb, Old Bay, 2 tablespoons bread crumbs, and mayonnaise in a medium bowl, being careful not to break up the lumps of crab.
Season with salt and white pepper to taste.
Carefully fold in the egg with a rubber spatula until the mixture just clings together. Add more crumbs if necessary. (see note).
Divide the crab mixture into four portions and shape each into a fat, round cake, about 3 inches across and 11/2 inches high.
Arrange the cakes on a baking sheet lined with waxed or parchment paper; cover with plastic wrap and chill at least 30 minutes. (The crab cakes can be refrigerated up to 24 hours.).
Put the flour on a plate or in a pie tin. Lightly dredge the crab cakes in the flour.
Heat the oil in a large, preferably nonstick skillet over medium-high heat until hot but not smoking.
Gently place chilled crab cakes in the skillet; pan-fry until the outsides are crisp and browned, 4 to 5 minutes per side.
Serve immediately with lemon wedges or dipping sauce.
Note: The amount of bread crumbs you add will depend on the moistness of the crabmeat. Start with the smallest amount, adjust the seasonings, then add the egg. If the cakes won't bind at this point, add more bread crumbs, 1 tablespoon at a time. If you can't find fresh jumbo lump crabmeat, pasteurized crabmeat, though not as good, is a decent substitute.