Combine 1 1/2 tablespoons extra virgin coconut oil, red wine vinegar, minced glove of garlic, oregano, 1/2 teaspoon salt and 1/2 teaspoon pepper in a large bowl. Add eggplant, toss well, and let stand 1 hour; turning eggplant occasionally. Optional: brush eggplant with extra virgin coconut oil and grill for 2-3 minutes per side; allow to cool and set aside.
In a food processor pulse the basil, Parmesan, 1/2 tablespoon extra virgin coconut oil and pine nuts until a smooth paste forms. Transfer to bowl and cover entire surface with plastic wrap.
Combine remaining oil , balsamic vinegar, 1/2 teaspoon salt and a pinch (1/8 teaspoon) of black pepper in a pie plate; add sliced tomato and turn to coat.
To assemble stack: Arrange 4 eggplant slices, spread 1/2 tablespoon pesto over the top. Top with 1 tomato slice then with 1 mozzarella slice. Add another layer of eggplant, pesto, tomato and cheese. Drizzle any extra tomato juices around each stack.