Start by cleaning the 2-pound fresh whole yellowtail snapper, removing any scales and insides as required. Place the fish in a shallow baking pan.

In a small bowl, combine minced garlic, finely minced Scotch bonnet or habanero pepper, and kosher salt to create a fragrant paste. Mix in chopped scallions, thinly sliced shallots, lime juice, and olive oil. Fill the fish cavity with fresh thyme and sliced onion, then generously coat the outside of the fish with the marinade. Cover and refrigerate for 1 hour.

While the snapper marinates, whisk together the egg yolk and Dijon mustard until combined. Gradually drizzle in 1 cup of vegetable oil while whisking vigorously to emulsify. Stir in lime juice, then season with salt and pepper to taste. Refrigerate until ready to serve.

Preheat the grill to a medium-high heat of 450°F. Lightly spray a fish basket to prevent sticking. Carefully place the marinated yellowtail snapper inside, secure it, and set on the grill. Cook for 10-12 minutes each side until the fish is opaque and flakes easily.

Transfer the Caribbean Grilled Yellowtail Snapper to a serving platter. Garnish with parsley and scallions, and serve hot alongside the garlic aioli and lime wedges.