In a medium bowl, whisk together 1/4 cup light mayonnaise, 1 large egg yolk, 2 teaspoons Old Bay seasoning, 1 tablespoon spicy brown mustard, 1/4 teaspoon hot sauce, and 1/8 teaspoon Worcestershire sauce until combined.
Gently fold in 1 pound fresh jumbo lump crab meat, then fold in 1/2 cup panko breadcrumbs. Season the mixture with 1/4 teaspoon salt and 1/4 teaspoon freshly ground black pepper. Cover and refrigerate for 1 hour to firm up.
While the crab mixture chills, make the avocado aioli: in a food processor or blender, process 1 large avocado, 2 tablespoons sour cream, 1 tablespoon fresh lime juice, and 1/4 cup water until smooth. Stir in 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper. Cover and refrigerate until ready to use.
Preheat the oven to 350°F. Line baking sheets with parchment paper.
Peel the 3 large green plantains: trim the ends, then use a vegetable peeler (or a sharp knife) to remove the peel and to slice each plantain lengthwise into thin strips (you should get about 40 slices total).
Arrange the plantain strips in a single layer on the prepared baking sheets. Lightly brush both sides of the strips with vegetable oil. Bake for about 3 minutes—just until the plantain strips become pliable but not browned. Remove from the oven and let cool slightly so they are easy to handle.
Place a sheet of plastic wrap on your work surface. Arrange 4 plantain strips in a spoke pattern on the plastic wrap. Scoop about 1/3 cup of the chilled crab mixture into the center and gently pat into a compact round cake. Wrap the plantain strips around the cake and pull the plastic wrap tightly to hold the shape. Repeat with the remaining plantain strips and crab mixture.
Refrigerate the wrapped crab cakes for at least 1 hour to set.
When ready to cook, unwrap the crab cakes and discard the plastic wrap. Pour enough vegetable oil into a large skillet to lightly coat the bottom and heat over medium-high until hot and shimmering.
Fry the crab cakes in batches, 3 to 4 minutes per side, until evenly browned and heated through. Avoid overcrowding the pan. Transfer cooked cakes to a paper towel–lined plate and gently pat to remove excess oil.
Top each crab cake with the chilled avocado aioli and serve warm.