Dice the onion, mince the garlic, slice carrots and celery, cut chicken into 1-inch pieces, roughly chop the spinach, and grate the Parmesan cheese fresh for the best results.
Heat olive oil in a large Dutch oven over medium-high heat, season chicken with salt and pepper, and cook in a single layer for 2–3 minutes per side until golden brown. Remove chicken to a plate and set aside.
Reduce heat to medium, add the onion to the same pot and cook for 3–4 minutes until softened, then stir in garlic for 30 seconds, followed by carrots and celery — sauté for 5 minutes, scraping up any browned bits from the bottom.
Pour in the chicken broth, add thyme, basil, oregano, salt, and pepper, then bring to a boil before reducing heat to medium-low and simmering for 5 minutes to soften vegetables and meld flavors.
Return the chicken (and any plate juices) to the pot, add the tortellini, and cook according to package directions — typically 7–9 minutes for refrigerated or 3–5 minutes for frozen — until pasta floats and is tender.
Reduce heat to low, slowly stir in the heavy cream, then add spinach and stir until wilted (1–2 minutes). Fold in the Parmesan until melted, taste for seasoning, and remove from heat.
Ladle into bowls ensuring each serving has chicken, tortellini, and vegetables, then garnish with fresh parsley and extra Parmesan. Serve immediately with crusty bread.