Heat olive oil in a large pot over medium-high heat. Add ground beef and cook for 3-4 minutes, breaking it apart with a spoon as it cooks, until it's no longer pink and beginning to brown. Transfer the cooked beef to a plate, leaving about 1.5 tablespoons of the rendered fat in the pot—this flavorful fat will be your cooking base.
With the pot still over medium heat and the reserved beef fat as your base, add the diced onion, sliced celery, and sliced carrots. Cook for 7-8 minutes, stirring occasionally, until the vegetables begin to soften and the onions become translucent. In the final minute, add the minced garlic and cook for about 1 minute, stirring constantly, until fragrant.
Pour in the chicken broth, diced tomatoes with their juices, and tomato sauce. Add the cooked ground beef back into the pot. Sprinkle in the Italian seasoning and red pepper flakes, then season with salt to taste. Stir everything together to combine and bring the soup to a gentle simmer.
Once the soup reaches a simmer, reduce the heat to medium or medium-low and cover the pot partially with a lid. Let it simmer gently for 15 minutes, allowing the flavors to meld together.
Add the cheese tortellini directly to the simmering soup and stir gently to separate any that might be stuck together. Return to a gentle simmer and cook for 4-7 minutes, depending on whether you're using fresh or frozen tortellini.
Remove the pot from heat and stir in the fresh spinach and chopped parsley. The residual heat will gently wilt the spinach in about 1-2 minutes. Give the soup a final stir and taste for seasoning, adjusting salt and red pepper flakes as needed. Ladle into bowls and serve immediately.