Bring a large pot of water to a boil, season with salt. Cook pasta 1 minute less than packaged directions. Drain pasta and toss with 1 tablespoon of olive oil in a large mixing bowl. Place pasta on a sheet tray to cool down.
Season eggplant with 1 tablespoon of olive oil; add salt and pepper to taste. Roast eggplant in the oven for about 10 minutes, or until golden brown, then remove from the oven and cool down.
Combine basil, pine nuts, salt and pepper in a blender, pulse for 5 seconds. Drizzle in remaining olive oil then add ice cubes and puree.
Remove pesto from the blender and transfer to a large bowl. Add lemon juice, pasta, and eggplant to pesto, toss to combine. Top with shredded parmigiano cheese before serving.