In a large stockpot over medium heat, heat the oil until it shimmers, about 2 minutes, then add the onion, garlic, and carrots, and saute for 5 minutes or until the vegetables are slightly soft. Pour in the chicken stock, increase the heat to high, and bring to a boil. Add the peas, tortellini, and corn and cook for 12 minutes, or according to the package directions for the tortellini.
Remove the stockpot from the heat and add the spinach, stirring until it wilts. To serve, spoon the soup into bowls and top with grated Parmesan cheese.