If using rotisserie chicken, shred to make about 3 cups and set aside; to poach, place two boneless skinless chicken breasts in a pot, cover with stock, bring to a gentle simmer and poach until 165°F, about 12–15 minutes, then shred after resting 5 minutes.

Heat olive oil in a 6-quart Dutch oven over medium heat; add diced onion and carrots and cook until translucent and slightly softened, about 6 minutes, then add diced celery, minced garlic, and Italian seasoning and cook 1–2 minutes until fragrant.

Pour in chicken stock and crushed tomatoes (or dissolved tomato paste), bring to a gentle simmer, add shredded chicken and frozen peas if using, and simmer uncovered for 8–10 minutes so flavors meld and vegetables become tender-crisp.

While the soup simmers, cook tortellini in a separate pot according to package directions until al dente; drain and set aside to keep texture intact.

Stir baby spinach and chopped parsley into the simmering soup, season with salt and pepper, then either add cooked tortellini to the pot off heat or spoon soup into bowls and top each with freshly cooked tortellini; finish with grated Parmesan if desired.