Brine Shrimp: Dissolve ¼ cup salt in 1 quart cold water in large container. Using kitchen shears or sharp paring knife, cut through shell of shrimp and devein but do not remove shell. Using paring knife, cut ½-inch-deep slit in each shrimp, taking care not to cut shrimp in half completely. Submerge shrimp in brine, cover, and refrigerate for 15 minutes.

Prep Vegetables: While shrimp brines, slice scallions thin; keep white and green parts separate. Mince garlic. Cut away peel and pith from oranges. Quarter oranges, then slice crosswise ½ inch thick. Remove core from cabbage and slice thin crosswise. Shred ½ cup basil.

Make Dressing: Whisk 2 tablespoons oil, vinegar, scallion whites, ¼ teaspoon salt, and 1/s teaspoon pepper together in large bowl; set aside.

Flavor Shrimp: Adjust oven rack 4 inches from broiler element and heat broiler. Combine fennel seeds, pepper flakes, scallion greens, garlic, and remaining ½ cup oil in large bowl.

Remove shrimp from brine and pat dry with paper towels. Add shrimp to oil mixture; toss well, making sure oil mixture gets into interior of shrimp. Arrange shrimp in single layer on wire rack set in rimmed baking sheet.

Cook Shrimp: Broil shrimp until first side is opaque and shells are beginning to brown, 2 to 4 minutes, rotating sheet halfway through broiling. Flip shrimp and continue to broil until second side is opaque and shells are beginning to brown, 2 to 4 minutes, rotating sheet halfway through broiling. Transfer shrimp to serving platter.

Finish Dish: Add orange pieces, cabbage, and basil to dressing in bowl and toss to combine. Serve with shrimp.