Heat the oil in a saute pan over medium high heat. Saute celery and 1/3 cup green onions until soft. Set aside.
Preheat the broiler.
In a large bowl, mix the cracker crumbs, 1/4 cup green onions, egg, parsley, seafood seasoning, and salt. Add the sauteed onion and celery, and the crabmeat and gently mix.
Form the crab mixture into 8 cakes using either a round mold or your hands. Place the cakes, not touching, on a metal baking sheet. Broil the crab cakes for about 4 minutes. Gently turn them over, careful not to break them, and broil the other side. At the end of 8 minutes, they should be nicely browned.
Heat stovetop grill on medium high heat. Alternately, you can make this recipe on an outdoor grill. "Crown" the buns by cutting off the rounded tops with a bread knife. This will leave you with 8 buns with flat tops. Cut in half lengthwise, if not already split. Brush the outsides with olive oil.
On the inside of the top half of each bun, spread about 1 tablespoon of the basil sauce and 1/2 tablespoon of the onion relish. You can vary the amounts to your taste. Place a crab cake on the bottom half of the bun and cover with the top half of the bun.
Grill each sandwich for 1 to 2 minutes per side. While you grill, press down on the sandwich with a metal spatula. This will flatten the sandwich, and make pretty grill marks on the bun. The sandwich is done when it is lightly browned on each side. Cut the sandwiches into halves or quarters and serve.
Mix all ingredients in a food processor and set aside.
Toss the ingredients together in a small bowl and set aside.