Heat 1/4 cup of the oil in a large high-sided skillet over medium-high heat until it shimmers. Add the radicchio, cut side down; lightly sprinkle with salt and pepper and cook, undisturbed, until nicely browned on the bottom, about 2 minutes. Drizzle 1 tablespoon of the remaining oil onto the radicchio, flip, sprinkle lightly with salt and pepper and cook, undisturbed, until the second side is nicely browned, 2 minutes more. Reduce the heat to medium-low, cover and cook until the radicchio is very soft when pierced with a knife, 4 to 7 minutes. Use a slotted spoon to transfer pieces to a serving platter when done.
Reduce the heat to low and heat the remaining 3 tablespoons oil. Add the anchovies and garlic and cook, stirring, until the garlic is lightly toasted and the anchovies melt, about 2 minutes. Stir in the lemon zest and juice and a good amount of pepper. Taste and season with salt and pepper if necessary. Pour the sauce over the radicchio and serve with crusty bread.
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