Bring the vegetable stock or water to a boil in a medium pot or large high-sided sauté pan. Once simmering, season with salt and then add half of the leek and poach, stirring occasionally, until tender but not mushy, 9 to 11 minutes. With a slotted spoon, transfer the leeks to a baking sheet, spread them out and let cool.
Add the lobster to the simmering broth and cook until thoroughly opaque, 5 to 7 minutes. Turn off the heat and, using a slotted spoon, transfer the lobster to a plate.
While the lobster and leeks are cooling, chop all of the tarragon leaves and stems. Place all but 1 tablespoon (set aside) of the chopped tarragon in a food processor or blender; add 5 tablespoons olive oil, 2 tablespoons lemon juice and the garlic. Pulse until you have a coarse purée, then transfer to a small bowl and season with salt and pepper.
In a medium bowl, whisk the remaining 2½ tablespoons olive oil, vinegar and mustard to combine. Season with salt and pepper. When the leeks are cool, add them to the bowl and toss to coat. In another bowl, combine the mayo, celery, shallot, remaining 1 tablespoon tarragon and remaining 1½ teaspoons lemon juice. Mix with a fork or whisk to combine, then add the cooked lobster meat. Toss again to coat the lobster, taste and season with more salt and pepper, if desired.
When ready to serve, use a spoon to drizzle the tarragon purée on the base of a platter, followed by a dollop of the crème fraîche. Arrange the leeks in vinaigrette over the top, followed by the lobster salad. Sprinkle everything with flaky salt, drizzle with olive oil, top with the chervil or parsley and serve.