Combine 3 cups shredded green cabbage; ½ red onion, thinly sliced, rinsed, and dried; ½ red, orange, or yellow bell pepper, cut into thin strips; 2 tablespoons lime juice; and ½ teaspoon table salt in bowl; set aside.

Pulse ¾ cup fresh parsley leaves, ¾ cup fresh cilantro leaves, 1 minced garlic clove, ¾ teaspoon red pepper flakes, and ⅛ teaspoon salt in food processor until coarsely chopped, about 5 pulses.

Add ¾ cup mayonnaise and 1 tablespoon red wine vinegar and pulse until mixture is combined but not smooth, about 5 pulses, scraping down sides of bowl as needed.

Transfer sauce to bowl; do not clean food processor.

Add 1 pound skinless cod fillets, cut into 1-inch pieces, to food processor and pulse until coarsely chopped into ¼-inch pieces, about 5 pulses; transfer to large bowl.

Gently fold in 6 tablespoons sauce, ¾ cup panko bread crumbs, and remaining ¼ teaspoon salt.

Spread remaining ¾ cup panko bread crumbs in shallow dish.

Using your lightly moistened hands, divide cod mixture into 4 equal portions, then gently shape each portion into 1-inch-thick cake, about 3½ inches in diameter.

Working with 1 cake at a time, dredge in panko, pressing lightly to adhere; transfer to plate.

Heat ¼ cup vegetable oil in 12-inch nonstick skillet over medium heat until shimmering.

Cook cakes until golden brown, 5 to 7 minutes per side, reducing heat as needed if panko is browning too quickly.

Transfer cakes to paper towel–lined plate and let drain, about 30 seconds per side.

Spread remaining sauce evenly over 4 toasted hamburger bun tops.

Transfer cod cakes to bun bottoms, top with slaw and bun tops, and serve.