01 - Preheat grill to medium heat (approximately 375°F).
02 - Season both sides of halibut fillets generously with kosher salt and freshly ground black pepper.
03 - Place a heatproof skillet or grill-safe pan over medium heat. Add olive oil and sauté finely chopped shallot and minced garlic until fragrant, approximately 1 minute.
04 - Add chopped tomatoes to the pan. Cook while stirring continuously until tomatoes begin to break down, about 3-4 minutes.
05 - Pour in dry white wine and fresh lemon juice. Let the mixture simmer until slightly reduced, 2-3 minutes.
06 - Reduce heat to low. Gradually whisk in unsalted butter one tablespoon at a time until sauce achieves a silky consistency. Stir in chopped fresh basil.
07 - Carefully place seasoned halibut fillets into the tomato-butter sauce. Spoon sauce generously over the top of each fillet.
08 - Transfer the skillet 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, transfer halibut directly onto grill grates for 1 minute per side to create attractive grill marks.
10 - Serve immediately with extra tomato-butter sauce spooned over fillets. Garnish with fresh basil leaves and lemon wedges.