Place a rack in top third of oven; preheat to 450°. Toss carrots and olive oil on a large rimmed baking sheet. Season with kosher salt. Roast carrots until lightly charred around the edges and just-tender in the center. 15–18 minutes. Let cool slightly.
Meanwhile, cook shallots, nori, garlic and butter in a small saucepan over medium heat, stirring often, until butter is browned and nutty-smelling and shallots are golden, 6–7 minutes.
Transfer carrots to a plate. Spoon butter dressing over. Drizzle with lime juice and season with sea salt.