Clean the shrimp: remove the carapace, head and gut, then rinse quickly under fresh running water and pat dry with paper towels. With a well-sharpened chef's knife make the tartare by cutting the shrimp into not-too-small cubes. Season with a drizzle of oil and a few chopped mint leaves. Set aside in a cool place.
Cook the sunflowers in boiling salted water, drain them al dente and transfer them to a pan with a knob of butter, then quickly toss over high heat along with the lime juice and a few tablespoons of the cooking water. Distribute the sunflowers in two soup plates, then arrange a generous spoonful of tartare in the center of each plate. Top with fillets of lime zest, a drizzle of raw oil, and a few fresh mint leaves.
Serve immediately.