Preheat oven to 400F (or whichever temperature is recommended by your pizza crust recipe).
Heat 1 Tbsp olive oil in a large frying pan over medium-low heat. When oil is warm, sautee onion until soft and brown, approximately 15 minutes. Once onion has browned, add minced garlic, and cook one minute more. Then remove onion and garlic from pan.
Add 2 Tbsp olive oil to frying pan. Once warm, add the eggplant, red pepper, and balsamic vinegar, cover, and sautee for 10 - 15 mins over low heat until all the vegetables are soft. Remove from heat.
Spread the sauce thinly over your pizza base. Spread your cooked vegetables evenly across the base. Cover with mozzarella cheese and cherry tomatoes.
Sprinkle pizza with salt and pepper.
Place pizza into preheated oven for 15 mins, or whatever is recommended by your pizza crust recipe.
After removing cooked pizza from oven, cover pizza with fresh basil leaves. Serve warm.