Preheat the oven to 400°F (204°C). Line a baking sheet with parchment paper.
Prepare the salt crust by mixing kosher salt, egg whites, and water in a bowl until the mixture resembles wet sand.
Stuff the cleaned fish cavity with lemon slices, garlic, thyme, green onions, and black pepper.
Spread a thin layer of the salt mixture on the baking sheet. Place the fish on top and completely cover it with the remaining salt mixture, pressing gently to seal.
Bake the fish for 30–35 minutes, depending on the size, until the crust is firm and the fish reaches an internal temperature of 145°F (63°C).
While the fish cooks, prepare the escovitch vegetables. Heat olive oil in a saucepan over medium heat. Add the onions, carrots, bell peppers, Scotch bonnet pepper, thyme, and allspice berries. Cook for 2–3 minutes until the vegetables begin to soften but still keep some crunch.
Add the vinegar, water, brown sugar, salt, and black pepper. Simmer for 3–5 minutes until the vegetables are slightly tender and the flavors combine.
Remove the fish from the oven and carefully crack open the salt crust. Brush away excess salt and gently remove the skin and bones.
Transfer the fish to a serving platter and spoon the warm escovitch vegetables with their pickling liquid over the top.
Serve immediately with extra lime wedges, rice and peas, fried plantains, or Jamaican festival bread.