Rub the garlic on the bread slices. Grill bread on Tuscan grill.
Slice eggplant into 1/4-inch rounds. Salt and dry between paper towels. Cut radicchio into quarters. Rub both radicchio and eggplant with olive oil. Put on sheet pans and cook in a preheated 350 degree F oven. Cook until radicchio is wilted (or just grill). Cook eggplant until it begins to brown (about 10 to 15 minutes).
Roast 1 or 2 heads of garlic. Cut across top to expose all cloves (cut 1/3 way down). Drizzle with olive oil and sprinkle with thyme. Bake in a preheated 350 degree F oven, covered for about 40 minutes. Remove cover, put pat of butter on it. Bake for 20 more minutes until it caramelizes. When cooked, grab whole head of garlic and squeeze into food processor.
Add eggplant and radicchio into food processor. Pulse until mixture becomes a coarse puree. Add salt, pepper and olive oil, to taste.