In a large Dutch oven or heavy soup pot, melt butter with olive oil over medium heat. Add the diced onion, sliced carrots, and chopped celery. Cook for 5 to 6 minutes, stirring occasionally, until vegetables soften and onions are translucent.

Add minced garlic, dried oregano, and dried thyme. Cook for 1 minute until fragrant. Sprinkle flour over the vegetables and stir continuously for 1 minute to cook out raw flour taste. Slowly pour in the chicken broth while whisking gently to create a smooth, lump-free base.

Bring broth to a gentle simmer. Add the refrigerated cheese tortellini and shredded chicken. Cook uncovered for 4 to 5 minutes at a gentle simmer until tortellini are tender and float to the top.

Reduce heat to low. Stir in heavy cream and fresh baby spinach. Simmer for 2 minutes until spinach wilts into the broth. Remove pot from heat, stir in freshly grated Parmesan cheese, and season with salt and black pepper to taste. Let rest 2 minutes before serving.