01 - Preheat grill to medium heat (approximately 375°F).
02 - Season halibut fillets generously with kosher salt and freshly ground black pepper on both sides.
03 - Place 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 skillet. Cook, stirring frequently, until tomatoes begin to break down, approximately 3-4 minutes.
05 - Pour in dry white wine and fresh lemon juice. Let mixture simmer until slightly reduced, 2-3 minutes.
06 - Reduce heat to low. Gradually whisk in unsalted butter, 1 tablespoon at a time, until sauce becomes silky and emulsified. Stir in chopped fresh basil.
07 - Carefully place seasoned halibut fillets into the tomato-butter sauce. Spoon sauce over the top of each fillet.
08 - Transfer skillet to preheated grill and close lid. Poach fish in sauce for 8-12 minutes, until fillets are just opaque and flake easily with a fork.
09 - For enhanced flavor and presentation, finish halibut directly on grill grates for 1 minute per side to achieve char marks.
10 - Serve immediately, spooning extra tomato-butter sauce over each fillet. Garnish with fresh basil leaves and accompany with lemon wedges.