The trick to making eggplant is to set it out on towels (paper is fine) to let it dry for an hour before cooking it.
Sprinkle salt on a towel.
Slice the eggplant in thick slices 1/2 inch thick.
Place on the towel and sprinkle more salt on the tops.
Lay a second towel on the top.
Cut the Roma tomatoes in half an scoop all the seeds out.
Chiffonade your basil and set aside.
Slice the mozzarella cheese.
Before grilling the eggplant drizzle or brush it with some of the olive oil (not too much or you will have a flare up on your grill). You can brush on a bit more as it is cooking. The eggplant absorbs it in quite well.
Wrap the garlic (skin still on) in aluminum foil and drizzle with olive oil. Place it on the grill at a high level or off to the side. You want it to cook but not burn.
Place the tomatoes on the grill and keep a close watch on them they cook quickly. Turn them as needed. You want them to still be firm enough to pick up. You are only grilling them to reduce the acidity and bring out their flavor.
Eggplant is done when you can poke it with a fork and feel that it is no longer tough (like the consistency of a cooked potato).
Rough chop your cooked tomatoes and place in a bowl. Set aside.
Pinch or pull the garlic out of its skins and add it to the bowl (it should be mushy).
Add in 3/4 of the basil, reserving some for plating.
Mix in your balsamic and olive oil.
Add the salt to taste.
Plate by placing the eggplant slice first, then the mozzarella, and then a scoopful of the tomato mixture. Sprinkle the top with a pinch of the fresh basil