Prepare the following, adding each to the same bowl as you complete it: Dice 1 medium yellow onion (about 1 ½ cups). Peel and dice 1 medium carrot (about ½ cup). Dice 1 medium stalk celery (about ⅓ cup). Mince 3 garlic cloves.
Heat 2 tablespoons olive oil in a Dutch oven over medium heat until shimmering. Add the vegetables, 1 ½ teaspoons Italian seasoning, 1 teaspoon kosher salt, and ¼ teaspoon black pepper. Cook, stirring occasionally, until softened, about 5 minutes. Add 3 tablespoons all-purpose flour and stir to coat the vegetables until no dry streaks remain. Cook for 1 to 2 minutes.
Add 1 (32-ounce) carton low-sodium vegetable or chicken broth and 1 (28-ounce) can fire-roasted crushed tomatoes and stir to combine. Bring to a boil over medium-high heat. Reduce the heat to maintain a gentle simmer and cook for 15 minutes to allow the flavors to meld. Meanwhile, finely grate 1 ounce Parmesan cheese (about ½ cup lightly packed) if needed, or measure out ⅓ cup store-bought.
Add 1 (8- to 9-ounce) package refrigerated cheese tortellini and cook for 1 minute less than the package instructions. Remove the pot from the heat. Add the Parmesan cheese, ½ cup heavy cream, and 5 ounces baby spinach, and stir to combine. Let sit until the spinach is wilted, about 1 minute. Add 2 teaspoons balsamic vinegar and stir to combine. Serve topped with more Parmesan cheese if desired.
