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