Preheat the oven to 400° and line two sheet pans (use small sheet pan for cherry tomatoes) with parchment paper.
Slice the eggplant into ½-inch rounds. You’ll need 12 slices total and arrange them in a single layer on the larger baking sheet. Place the halved cherry tomatoes on the smaller baking sheet.
Drizzle 2 tablespoons of olive oil over the eggplant slices and 1 tablespoon over the cherry tomatoes. Roast tomatoes for 15-20 minutes and eggplant slices for 25–30 minutes, flipping the eggplant slices halfway through.
Once eggplant and tomatoes are tender, take out of the oven and keep the oven on.
To assemble: place 6 eggplant slices in the baking dish. Sprinkle with ¼ tsp salt then spread 1-2 teaspoon of pesto on each slice. Add 3–4 roasted cherry tomato halves on top and sprinkle with cheese. Repeat this layering process to build the stacks.
Return the assembled stacks to the oven and bake for 5–7 minutes, or until the cheese is melted.
Let the stacks cool for 5–10 minutes before serving. Garnish with chopped parsley or fresh basil.