Step 1Grill the onions: Heat a grill or grill pan over medium-high heat until hot. Lightly brush the green onions with oil, then grill, turning every minute or so, until charred on all sides. Remove from heat and set aside until cool, then slice crosswise into small rings.
Step 2In the bowl of a stand mixer fitted with the whisk attachment, or in a large bowl using a hand mixer, beat together the egg yolk, salt, mustard, sugar, lemon juice, cane vinegar and Worcestershire sauce until incorporated. With the mixer running, slowly add the oils until you reach a mayonnaise-like consistency. Fold in the green onions and sweet pickle relish. Cover and refrigerate until ready to use. This makes about 1 cup tartar sauce, which will keep, covered and refrigerated, up to 5 days.
Step 1In a medium bowl, combine the tomato, red onion and basil, seasoning with salt and pepper to taste. Cover and refrigerate at least one hour before using, to give the flavors time to marry.
Step 1In a large bowl, very gently combine the crabmeat, green onions, lemon juice, mayonnaise, salt, pepper and three-fourths cup bread crumbs, carefully folding the ingredients together to avoid breaking up the lumps of crabmeat. Divide the mixture into fourths, and mold each into a crab cake (if the crab cakes are too delicate to hold together, add the remaining bread crumbs to make them firmer). Flour both sides of each cake with the seasoned flour. The crab cakes can be made up to 1 day ahead and refrigerated, covered, until ready to cook. If making ahead, wait to flour the crab cakes until ready to cook.)
Step 1In a large sauté pan, heat the olive oil over medium-high heat until hot. Stir in the corn, bell and jalapeño peppers, onions and garlic, and cook until the vegetables are softened, 6 to 8 minutes. Stir in the flour and continue to cook, stirring constantly, until the flour begins to smell nutty, 2 to 3 minutes. Slowly stir in the milk and cream, and simmer, stirring constantly, until the liquid reduces and the mixture begins to thicken, about 20 minutes. (If it thickens too quickly, the mixture can be thinned with a little chicken broth or water.) Stir in the Worcestershire and hot sauce, along with the pepper, salt and cayenne pepper. Remove from heat and set aside.
Step 1Heat a skillet over medium-high heat until hot. Add a tablespoon or two of oil to lightly coat the bottom of the skillet, and gently place one or two crab cakes in the pan (this will need to be done in batches). Brown the crab cakes on one side, then carefully flip over and brown the other side. Remove the crab cakes to a rack, and continue cooking until all of the crab cakes are done.
Step 2On each of 4 plates, ladle one-fourth of the corn maque choux. Place a crab cake in the center of each and spoon 2 tablespoons of the tartar sauce on top of the cake. Finish each dish with a tablespoon of tomato relish and garnish with green onions. Serve immediately.