How to Make It
In a large, deep skillet, heat 1/4 cup of the olive oil. Add the tomatoes and tomato paste and cook over moderate heat, stirring occasionally, until the tomatoes just start to soften, about 5 minutes. Add the lemon quarters, tarragon, parsley, vinegar and the remaining 1/4 cup of olive oil. Cook over moderate heat, stirring occasionally, until the tomatoes are very soft and the dressing is saucy, about 15 minutes. Discard the lemon quarters. Season with salt and pepper and let cool slightly.
In a large ceramic baking dish, whisk the lemon juice with the olive oil and season with salt and pepper. Add the quartered radicchio and turn to coat; let stand for 15 minutes.
Preheat a grill pan and the broiler. Season the radicchio with salt and pepper and grill over high heat, turning, until lightly charred and just starting to wilt, about 3 minutes. Return the radicchio to the baking dish and sprinkle the marjoram and goat cheese on top. Broil 8 inches from the heat until the goat cheese is just softened, 1 to 2 minutes. Transfer the radicchio to a platter. Spoon some of the dressing on top and serve, passing the rest of the dressing at the table.