Heat the olive oil in a large soup pot over medium heat. Add in the onion, carrots, celery, bell pepper, and garlic; season with a fat pinch of salt and pepper. Cook, stirring occasionally, until the veggies soften up slightly, around 3-4 minutes.
Add in the oregano, paprika, thyme, and Italian seasoning; continue cooking until the spices become fragrant, another 1-2 minutes.
Pour in the chicken broth and tomato passata; increase the heat the high.Bring the soup to a boil, add in the pearl barley, then immediately decrease the heat to medium and cover with a lid. Let the soup simmer away until the barley is cooked through, around 45-65 minutes depending on your particular barley.
Uncover and add in the turkey, baby spinach, and parsley. Continue cooking until the turkey is heated through and the parsley is wilted, another 6-8 minutes. Taste and adjust the seasoning with more salt and pepper, if needed.