Dissolve 2 tablespoons kosher salt in a large bowl of water. Add the radicchio and soak, 45 minutes, using a plate to keep it submerged. Drain the radicchio, shake off any excess water and pat dry.
Meanwhile, puree the garlic, anchovies and olive oil in a mini food processor. Transfer the mixture to a small saucepan and cook over low heat until golden and bubbly, about 5 minutes; set aside until cool.
Return the garlic-anchovy mixture to the mini food processor. Add the butter, cream, truffle oil, parsley and lemon zest and blend until combined. Cover and refrigerate until ready to use.
Preheat the broiler. Brush a 9-by-13-inch flame-proof baking dish with about 1 teaspoon of the sauce. Brush 1 1/2 teaspoons of the sauce between the leaves of each piece of radicchio and arrange in the prepared baking dish. Top each piece with 2 more teaspoons sauce and broil until the radicchio is crisp and browned and the sauce is bubbly, 5 to 8 minutes. Sprinkle with sea salt and drizzle with olive oil.