Preheat oven: Set your oven to 400°F.
Sauté: In a medium saucepan or skillet, heat 1 tablespoon olive oil over medium heat. Add the shallot and sauté until soft and fragrant, about 3 to 5 minutes. Add the garlic during the last minute and stir often so it doesn’t burn.
Simmer: Add the cherry tomatoes, chicken broth, and ½ teaspoon salt. Simmer uncovered for 10 to 15 minutes, stirring occasionally, until the tomatoes begin to break down and most of the liquid has evaporated.
Finish Sauce: Remove from the heat and stir in the cubed butter and chopped parsley until melted and well combined.
Prepare Fish: Pat the halibut dry with paper towel and place it in a 9x9 baking dish.
Season: Season the halibut with salt and pepper, then drizzle very lightly with olive oil and fresh lemon juice. Flip each piece to coat both sides, then turn presentation side up.
Add Sauce: Spoon the garlic tomato butter sauce evenly over the halibut.
Bake: Cover the baking dish tightly with foil and bake for about 20 minutes, or until the halibut flakes easily with a fork. Baking time will depend on the thickness of the fish.
Serve: Garnish with extra fresh parsley and serve warm.