01 - Preheat grill to medium heat (375°F).
02 - Season halibut fillets with salt and pepper on both sides.
03 - Place a heatproof skillet 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. 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 seasoned halibut fillets into the tomato-butter sauce. Spoon sauce over the top.
08 - Transfer skillet to preheated grill and close lid. Poach fish in sauce for 8-12 minutes, until just opaque and flakes easily with a fork.
09 - For added flavor, finish halibut directly on grill grates for 1 minute per side to add grill marks.
10 - Serve immediately with extra tomato-butter sauce spooned over fillets. Garnish with basil and lemon wedges.