Special equipment: Place the halibut into a 9 by 13-inch baking dish.
For the fish:
To a mortar and pestle, add the kosher salt, lemon zest, and 2 tablespoons coriander seeds. Crush and season the fish on both sides. Reserve the lemon juice for the court bouillon.
Place a medium pot over medium-high heat. Add the shrimp shells and remaining coriander seeds, allowing the shells to saute and the coriander to toast. Add the shallots, garlic, and bay leaf. Toss to combine and season with salt. Squeeze in the juice of the lemons and add the squeezed lemons themselves. Pour in the beer, about 1 to 2 cups water, to cover and taste. Season with salt and freshly ground black pepper, to taste. Lower the heat and allow to simmer about 5 minutes. Strain through a fine mesh strainer over a bowl. Pour the court bouillon over the fish and cover with plastic wrap. This will fully poach the fish to a medium-rare to medium temperature without having to go into the oven or on the stove. Set aside for about 8 to 10 minutes.
For the vinaigrette:
Meanwhile, to a bowl, add the zest and juice of 1 lemon, minced shallot, minced garlic, salt, to taste, and whisk in about 1/2 to 2/3 cup extra-virgin olive oil to make a 2 to 1, fat to acid ratio. Taste and re-season, if needed. Stir in the freshly sliced tarragon leaves just before serving and set aside.
For the vegetables:
Thinly slice the beets and carrots on a mandoline. Add to a bowl and season with salt. Pour over the vinaigrette and chiffonade beet greens, and toss to combine.
Place the halibut onto a plate. Season the fish with sea salt and top with the baby vegetable salad. Drizzle the plate with extra-virgin olive oil and sprinkle with sea salt.