Heat olive oil in a large pot or Dutch oven over medium-low heat.
Add the chopped onion, celery, and carrots. Sauté until softened, about 8-10 minutes, stirring occasionally. Season with salt and pepper, a teaspoon of sugar, and a tablespoon of Italian seasoning. When tender, add the minced garlic cloves and simmer for 30 seconds.
Add in the tomatoes, roasted red peppers (juice from the jar as well), vegetable broth, and bay leaves. Pop in the parmesan rind if you’re using it. Let everything simmer for 20-30 minutes on low. (Don’t let the soup come to a boil.)
Mix the yogurt with 1/4 cup warm water. Adding the cold yogurt to the hot soup could cause it to curdle, so you want to temper the yogurt in.
Slowly pour the yogurt into the soup as you stir to fully incorporate it, creating a creamy broth.
Remove the bay leaf and parmesan rind. Ladle the broth to a high-powered blender (you’ll have to do this in batches, a few cups at a time) and blend until smooth.
Stir in the tortellini and the freshly chopped spinach, simmering over low heat until the tortellini is cooked through.
Give the soup a taste and adjust the seasoning as needed. Serve and garnish with fresh basil or fresh parsley, grated parmesan, a dollop of Greek yogurt, and some red pepper flakes if you like it a bit spicy!