Pan-Fry the Eggplant: Warm 3 tablespoons of oil in a dutch oven or heavy-bottomed pot over medium-high heat. Add the eggplant and 1/2 teaspoon salt and stir immediately. Pan-fry for 5 to 6 minutes, stirring occasionally, until the eggplant is translucent and browned. Remove the eggplant from the pot and set aside on a plate.
Veggies: Add the onion to the pot and sauté for 1 minute, scraping the bottom of the pot to remove any browned bits. Add the tomatoes, zucchini, yellow squash, and an additional generous pinch of salt. Mix well and sauté for 5 minutes, stirring occasionally.
Aromatics: Add the garlic, Italian seasoning, and paprika to the pot and stir well. Sauté for 1 to 2 minutes, until the garlic is fragrant.
Simmer: Add the chickpeas and vegetable broth to the pot and bring to a boil over high heat. Reduce the heat to medium and simmer for 10 minutes, stirring occasionally. If the stew gets too thick for your liking you can thin it out with additional vegetable broth or water.
Serve: Turn the heat to low and add the eggplant, stirring well. Once the eggplant has warmed, divide the stew between serving bowls and top with torn basil. Serve warm; leftovers will keep in the fridge for up to 5 days.