Preheat oven to 400 degrees. Line two large baking sheets with parchment paper.
Chop about ¼ inch off the narrow end of the garlic bulb to expose the bottoms of the cloves, and peel off the papery outer skin. Set aside.
Slice the eggplant into 12, ½-inch slices (see notes). Season each side with sea salt and freshly ground pepper. Spread out evenly over one of the baking sheets. Place the garlic head, chopped side down, on the same baking sheet. Place into the oven, and roast at 400 degrees for 20 minutes.
Prepare the tomatoes the same way you did the eggplant (see notes). Place the seasoned tomato slices on the second baking sheet.
After 20 minutes, remove the eggplant and garlic from the oven, and turn everything over. Place the eggplant/garlic back in the oven, Place the tomatoes on another oven rack, and cook everything for 15 minutes, or until the eggplant is browned on both sides and tender. (If the eggplant is only brown on one side, flip it once more and cook until both sides are browned. ) When the vegetables are cooked, remove them from the oven and allow them to cool slightly on the baking sheets until you can handle them.
Squeeze the garlic cloves out of their skins. Place the roasted garlic, cannellini beans and basil in a food processor, and process until creamy. Season with sea salt and freshly ground black pepper to taste.
Spoon some of the bean mixture onto each slice of eggplant (you can do this right on the baking sheet), evenly covering the top of each slice. When all of the eggplant slices are tipped with the bean mixture, use a spatula to gently lift a tomato slice onto the top of each eggplant slice. Some of the stacks will be a little narrower than others. Place 6 of the narrower stacks on top of 6 of the wider ones. You'll now have 6 stacks total, with 2 layers of bean mixture each.
Place the stacks back in the oven, and heat at 400 degrees for 5-10 minutes, or until hot.
For best results when stacking, choose tomatoes about the same width or slightly smaller than your eggplant. The eggplant will shrink after roasting.
I was only able to get 3-4 slices out of the heirloom tomatoes pictured here because of their wide, short shape. If you're unsure, play it safe and buy more tomato than you think you'll need.
You'll probably end up with some leftover eggplant and tomato. (I did.) I cubed the leftover eggplant, chopped the tomato, and saved it to use later in spaghetti sauce.