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 a heatproof skillet or grill-safe pan over medium heat. Add olive oil and sauté shallot and 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 white wine and lemon juice. Let the mixture simmer until slightly reduced, 2-3 minutes.
06 - Reduce heat to low. Stir in butter 1 tablespoon at a time, allowing each addition to melt completely before adding the next. Sauce should become silky and emulsified. Fold in chopped basil.
07 - Carefully place seasoned halibut fillets into the tomato-butter sauce. Spoon sauce 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 smoky flavor, carefully transfer halibut directly to grill grates for 1 minute per side to create grill marks.
10 - Serve immediately, spooning extra tomato-butter sauce over each fillet. Garnish with fresh basil leaves and accompany with lemon wedges.