Polenta is a dish made from coarsely ground corn meal, aka grits.
Bring milk, 3 cups of the broth and ¼ teaspoon each salt and pepper to a boil in a medium saucepan over high heat. Slowly whisk in grits. Reduce heat to medium and cook, whisking often, until thickened, 20 to 25 minutes. Stir in ¼ cup of the Parmesan until blended. Remove from heat and keep warm.
Heat oil in a large skillet over medium-high heat. Add shallots and cook, stirring occasionally, until softened, about 2 minutes. Add zucchini and eggplant; cook, stirring often, until slightly tender, about 3 minutes. Stir in chickpeas, tomatoes and remaining ¼ cup broth and ¼ teaspoon each salt and pepper; cover and cook, stirring occasionally, until tomatoes are softened, 5 to 6 minutes. Stir in basil. Divide grits mixture evenly among 4 shallow bowls; top evenly with vegetable mixture and remaining ¼ cup Parmesan.