01 - Preheat your grill to medium heat, approximately 375°F.
02 - Season both sides of each halibut fillet generously with kosher salt and freshly ground black pepper.
03 - Place a large, heatproof skillet or grill-safe pan over medium heat. Add olive oil and sauté the finely chopped shallot and minced garlic until fragrant, about 1 minute.
04 - Add the chopped tomatoes to the pan. Cook, stirring frequently, until they begin to break down, approximately 3-4 minutes.
05 - Pour in the dry white wine and fresh lemon juice. Allow the mixture to simmer until slightly reduced, about 2-3 minutes.
06 - Reduce heat to low. Gradually whisk in the unsalted butter, one tablespoon at a time, until the sauce achieves a silky, emulsified consistency. Stir in the chopped fresh basil.
07 - Carefully place the seasoned halibut fillets directly into the tomato-butter sauce. Spoon some of the sauce over the top of each fillet.
08 - Transfer the skillet to the preheated grill and close the lid. Poach the fish in the sauce for 8-12 minutes, or until the flesh becomes opaque and flakes easily when tested with a fork.
09 - For enhanced flavor and presentation, carefully transfer the fillets directly onto the grill grates. Finish for 1 minute per side to achieve attractive grill marks.
10 - Serve immediately, spooning the remaining tomato-butter sauce generously over each fillet. Garnish with fresh basil leaves and accompany with lemon wedges.