Pick over the crabmeat to remove any shells. Be gentle, as the lumps of crab are delicate and will fall apart. Set aside. Mix together the mayonnaise, seafood seasoning, scallions, basil, eggs, and salt and pepper. Pour mixture over the crabmeat and with your hands gently mix together. Sprinkle the bread crumbs over the crab mixture and continue to mix. Divide the mixture into 4 parts and mold the cakes with your hands (do not rinse off you hands between mixing and forming the cakes, as it is mixture on your hands that help the cakes stay together).
Refrigerate the cakes for at least 30 minutes.
Preheat the oven to 400 degrees F.
Paint the crab cakes with a miniscule amount of oil and sear in a hot oven-safe skillet or on a griddle top until lightly golden brown on both sides. The cakes have such little binder that you need to be careful when flipping them over so that they don't fall apart. Place the pan in the oven for about 5 minutes, or to heat through.
Variation: I prefer to use a grill with really good hardwood briquette or mesquite. You'll need a special rack accessory that can be found in any store that sells grills. I use a rack with little holes so the crab won't fall through into the fire. Make sure that the rack is well seasoned or the crab will stick to the grill. If you're good with a grill then go for it.
Serve with a red cocktail sauce and/or a flavored aioli.