01 - Preheat your grill to medium heat (about 375°F).
02 - Season halibut fillets with salt and pepper on both sides.
03 - Place a large, heatproof skillet or grill-safe pan over medium heat. Add olive oil. Sauté shallot and garlic until fragrant (about 1 minute).
04 - Add chopped tomatoes. Cook, stirring, until starting to break down (about 3-4 minutes).
05 - Pour in white wine and lemon juice; let simmer until slightly reduced (2-3 minutes).
06 - Reduce heat to low, stir in butter 1 tablespoon at a time until sauce is silky. Add chopped basil.
07 - Carefully place the seasoned halibut fillets into the tomato-butter sauce. Spoon sauce over the top.
08 - Transfer the skillet or pan to the preheated grill (close lid). Poach fish in the sauce for 8–12 minutes, until just opaque and flakes easily with a fork.
09 - Optional: For added flavor, finish the halibut directly on the grill grates for 1 minute per side to add grill marks.
10 - Serve immediately with extra tomato-butter sauce spooned over the fillets. Garnish with basil and lemon wedges.