A drizzle of tart apple molasses tames this elegant starter of charred radicchio stuffed with butter and bottarga. Radicchio rosso di Treviso can be substituted for Verona, but keep in mind that the head and leaves are less compact.
Stir together butter, bottarga, garlic, lemon zest, and ½ teaspoon kosher salt in a small bowl until combined. Transfer mixture to a piping bag or a ziplock plastic bag with a small corner snipped off. Set aside.
Trim and discard ½ to 1 inch from bottom of radicchio head, exposing the base of the leaves. Place your thumbs inside center of the trimmed end, and gently pull apart to expose more of the leaves, keeping head as intact as possible. Starting in center of radicchio and working outward, insert piping bag between inner layers of radicchio; pipe filling, rotating radicchio as you pipe to coat leaves with filling. Using kitchen twine, secure radicchio head at 2-inch intervals. Rub outside of radicchio with extra-virgin olive oil; sprinkle with remaining ¾ teaspoon kosher salt.
Preheat grill to very high (500°F and up). Place radicchio on oiled grates; grill, uncovered, rotating often, until charred and just softened, about 5 minutes. Remove from grill; discard twine.
Slice radicchio crosswise into 4 rounds. Drizzle each slice with molasses and smoked olive oil; sprinkle with flaky sea salt.
Radicchio can be filled up to 1 day ahead and stored in an airtight container in refrigerator.
Find bottarga di muggine at gustiamo.com; find smoked olive oil such as Castillo de Canena Smoked Arbequina online or at specialty food stores.