Spray a rimmed baking sheet with olive oil or cooking spray. Place eggplant slices onto sheet and spray tops with additional olive oil. Season with salt and pepper and roast for 20–30 minutes or until softened and just beginning to brown, turning slices over halfway through cooking time. Remove from oven and set aside. Lower oven temperature to 400°F.
While eggplant is baking, start caramelizing the onions. Heat olive oil in a large skillet over low heat. Add onions and a pinch of salt. Allow onions to slowly caramelize, stirring occasionally at first and more frequently once onions begin to brown. Depending on your stove, this could take anywhere between 30 minutes to an hour. Be patient—it's worth it! Remove from heat.
Place rolled-out puff pastry dough onto a baking sheet that's been lined with parchment paper. Bake for 10 minutes or until golden brown. Remove from oven and use a spoon or spatula to push down the center of the crust, leaving about a 1-inch margin on all sides.
Spread caramelized onions onto crust. Top with cheese, then roasted eggplant slices, olives, and red peppers. Return to oven and bake 5 minutes, or until cheese has melted. Scatter basil ribbons onto tart just before serving.
Craving more veg-friendly recipes? Shop our collection of vegetarian and vegan cookbooks, including our new Vegan Thanksgiving and Vegan Christmas cookbooks!