Hickory wood chips (about 2 handfuls), for smoking.
To make the vinaigrette:
Prepare a wok smoker by laying 2 layers of foil in the bottom of a wok. Add in 2 handfuls of the hickory wood chips, and set the smoker over high heat. Pour in the water. Wash, quarter, and seed the tomatoes. Pop them into a bamboo steamer.
Arrange the tarragon and shallots around the tomatoes. Place the steamer onto your smoking wok and cover with lid or foil, and let the ingredients smoke for 20 minutes.
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 side 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 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.