Put a rimmed baking pan in lowest rack in oven and preheat to 350°. Trim Brussels sprouts deeply enough to easily peel off outer leaves. Discarding ends, peel off leaves until sprouts are about half their original size. Set leaves aside and cut sprout hearts in half.
In a large bowl, gently toss halved sprouts with grapeseed oil and 1 tsp. salt. Using tongs, arrange sprouts on preheated baking pan, cut side down, in a single layer. Roast on lowest rack until cut sides are medium golden brown, about 20 minutes. Let cool until just slightly warm.
Meanwhile, bring a large pot of salted water to a boil and set a large bowl of ice and cold water next to the stove. Boil Brussels sprout leaves until bright green, about 20 seconds. With a slotted spoon, immediately transfer leaves to ice bath.
Squeeze water gently from leaves and lay on a kitchen towel. Pat dry with another towel.
Divide Tonnato Sauce among serving plates or spread about 1/4 in. thick on a platter. Arrange roasted sprout halves on tonnato, browned sides up.
In a large bowl, toss sprout leaves with lemon juice, Sunchoke Oil, and remaining 1/2 tsp salt. Arrange leaves over sprout halves. With a Microplane, grate bottarga over the entire plate. Top with chervil and finish with grinds of fresh pepper.
*You can find good bottarga on amazon.com and Japanese bonito flakes in the Asian aisle of your grocery store.
Make ahead: Peel off leaves up to 3 days before steaming; once steamed, they'll hold up to 1 day, chilled. Sprout halves may be blanched in boiling salted water just until tender, 2 to 3 minutes, then chilled up to 3 days. Brown them for about 5 minutes in a hot cast-iron skillet before serving.