How to Make It
Make the curtido: In a large bowl, toss together cabbage, carrot, 2 tablespoons salt, sugar, and oregano. Let stand 1 hour. Place mixture in a colander and gently press out excess moisture. Return mixture to bowl. Toss with vinegar and 2 tablespoons oil and let stand, covered, at room temperature for 2 hours; chill until ready to serve.
Make the pico de gallo: In a bowl, toss together tomatoes, onion, cilantro, jalapeño, lime juice, 2 tablespoons oil, and 2 teaspoons salt; let stand at room temperature until ready to serve.
Make the snapper: Preheat oven to 400°F. Using kitchen shears, remove fins, and remove tail if too large to fit on a large rimmed baking sheet. Place lime slices in cavity. In a large bowl, combine 8 cups salt, egg whites, and tequila, and whisk until the mixture has the consistency of wet sand. Combine 1/2 cup salt mixture and chile in small food processor, and process until chile is combined with salt, about 15 seconds. Add chile mixture to salt mixture, and stir well. Spread half of salt mixture on a large rimmed baking sheet. Place snapper on top. Cover snapper with remaining salt mixture, pressing to adhere and making sure sides are covered.
Bake in preheated oven until a thermometer inserted into the center of the fish registers 125°F, about 40 minutes. Remove from oven; let stand 10 minutes. Crack salt shell with the back of a large spoon and remove from fish in large pieces. Remove skin from fish. Carefully pick meat from top half of fish down to the backbone. Remove backbone, ribs, and any parts of the fins that are still present along the ridge of the back. Pick remaining meat from fish and place meat in a serving bowl. Serve with curtido, pico, lime wedges, tortillas, and avocados.