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Wash, quarter, and seed the tomatoes. Pop them into a bamboo steamer.
Transfer the tomato-shallot mixture to a big pitcher, and blend with an immersion blender or use a regular blender. Gradually, add the olive oil in a thin stream, as you are blending to achieve a nice consistency. Season with a pinch of salt and some freshly cracked black pepper.
To make the halibut: Preheat an oven to 375 degrees F. Liberally sprinkle your halibut fillets with coarse salt and fresh cracked black pepper.
Add just enough oil to coat the bottom of a pan, and set it over fairly high heat.
Add the halibut fillets to the hot pan, skin side down. Once the first sides has browned nicely, about 3 to 4 minutes, flip them over and continue cooking for another 3 minutes. Then, slide the pan into the oven for about 5 minutes to finish cooking. The finished halibut should to be firm to the touch and snowy white in color, but since it is a lean fish, it will dry out if overcooked.
Ladle a pool of the vinaigrette into the bottom of a deep plate, top with a piece of halibut and a few baby greens, if using. Alternatively, you could use arugula tossed with sliced shallots, as a garnish.