Slice Italian bread info 8 thick slices. Slice each tomato into 4 slices.
Remove some of the skin from the eggplant, leaving the rest of the skin on for a striped look. Slice the eggplant into eight 1/2-inch rounds.
Heat olive oil in a skillet over medium heat. Season eggplant with salt and pepper; cook until soft, about 5 minutes per side. Watch that it does not burn. Remove to a plate and set aside.
Spread ricotta over 4 slices of bread. Top each with 2 eggplant slices and 2 tomato slices. Season tomatoes with salt and pepper. Tear 2 basil leaves over each sandwich. Add 4 slices of fontina cheese. Spread butter over the remaining slices of bread and place over the cheese, buttered sides up.
Melt remaining butter in a large skillet over medium heat. Add sandwiches to the skillet with the dry side down. Cover with a piece of foil and place a heavy pan on top. Toast sandwiches for 3 to 4 minutes. Flip over and cover again. Cook until cheese is melted, 3 to 4 minutes more.