To prepare the lobster, combine water, Chardonnay, salt, lemon juice, thyme and bay leaves to make poaching liquid. Bring liquid to a boil; cook lobsters for six minutes. Plunge lobster in ice bath to arrest cooking. Reserve lobster poaching liquid. When lobsters are cool enough to handle, remove tails and slice in half; remove claw meat and reserve.
Blanch greens for 2-3 minutes in lobster poaching liquid, until tender. Refresh greens in ice bath; remove excess water. Wrap one portion of the lobster tails in cabbage and one in chard.
Preheat oven to 360°. Melt butter and olive oil over medium heat. Place potatoes cut side down in the oil and butter and roast for 14 to 16 minutes, turning after 6 minutes. Season, add thyme and reserve warm.
For the chanterelle yuzu sauce, sauté shallots in 1 tsp butter until they are just softened but have not taken color. Add chanterelles and sauté over medium-high heat until they have just begun to color and very little liquid remains. Deglaze pan with yuzu and white wine; reduce to 2 tablespoons. Add cream, bring to a simmer and whisk butter into reduction, one cube at a time. Salt and pepper to taste.
To serve, warm lobster in chanterelle sauce and arrange over fingerlings. Sauce again with the chanterelles and garnish with tarragon or marjoram.