Heat the olive oil and butter in a large heavy bottomed Dutch oven or soup pot over medium heat. Add the diced yellow onion, chopped carrots, and sliced celery. Cook for about five to six minutes, stirring occasionally, until the onions turn translucent and the carrots begin to soften.

Add the finely minced garlic to the pot. Stir constantly for about sixty seconds until the kitchen fills with an irresistible, sweet garlic aroma. Sprinkle the all purpose flour over the vegetables and stir continuously for two minutes to cook out the raw flour taste.

Slowly pour in the low sodium chicken broth while whisking gently to smooth out any small flour lumps. Add the bay leaf, thyme, and rosemary. Bring the liquid to a gentle boil over medium high heat.

Reduce the heat to medium low, cover the pot partially, and let it simmer gently for ten to twelve minutes until the vegetables are completely fork tender.

Stir in the shredded cooked chicken breast and lower the burner setting. Pour in the heavy cream, stirring softly as the broth transforms into a luscious, milky golden hue. Allow the chicken to warm through for three minutes.

Remove the pot from the direct heat source. Slowly whisk in the freshly grated parmesan cheese, a small handful at a time, allowing each addition to melt completely into the hot broth before adding the next. This prevents the cheese from clumping.

Stir in the fresh baby spinach leaves. They will wilt down into tender green ribbons within sixty seconds in the residual heat. Discard the bay leaf. Taste the broth and season generously with salt and freshly cracked black pepper.

Ladle the steaming soup into deep cozy bowls. Top with an extra pinch of grated parmesan and a sprinkle of fresh parsley if desired. Serve immediately with warm crusty bread.