Heat the oil in a large Dutch oven until shimmering. Add the onion and sauté until softened, about 3 minutes. Add the orzo and garlic, season with salt and pepper, and sauté until fragrant, about 1 minute. Stir in the broth, tomatoes, and chickpeas and bring to a boil. Cover, reduce to a simmer, and cook, stirring frequently so that the orzo doesn’t stick, until most of the liquid is absorbed - about 10 minutes or according to package instructions. Stir in the Parmesan cheese. Taste and season with salt and pepper as needed. Garnish with the chopped basil and additional grated cheese.