In a mason jar, combine oil, garlic Kosher salt & pepper. Ass seasoning to your preference. You do want the oil flavorful. Allow the oil to sit for at least 30 minutes and up to 6 hours.
Slice the ends of the eggplant off and then cut into 1/4 to 1/2 inch-thick slices (rounds).
Brush both sides of your eggplant slices/rounds with the seasoned oil. You may also want to sprinkle just a bit more S & P on the slices/rounds.
Slice your Mozzarella into rounds.
Heat your grill to high, once hot place eggplant directly on the grill. Cook for 3 minutes, flip and cook until almost done to your liking.
With about 1-2 minutes to go, add slices of Mozzarella to each eggplant round and cook until just melted.
Assemble stacks atop warm sauce, top with Basil, additional seasoning and additional sauce to your liking.