In a large Dutch oven or stockpot, heat the olive oil and butter over medium heat. Add the diced onion, carrots, and celery (the mirepoix). Cook, stirring occasionally, until softened, about 6-8 minutes.

Add the minced garlic and dried thyme. Cook for another minute until fragrant, being careful not to burn the garlic.

Sprinkle the all-purpose flour over the vegetables and stir continuously for 1 minute to cook out the raw flour taste. This will create a roux to thicken the soup.

Slowly whisk in the chicken broth, a little at a time, to avoid lumps. Once all the broth is incorporated, add the bay leaf. Bring the mixture to a gentle simmer.

Carefully place the whole chicken breasts into the simmering broth. Reduce the heat to low, cover, and let simmer for 15-20 minutes, or until the chicken is cooked through and no longer pink inside.

Once cooked, remove the chicken breasts from the pot and set them on a cutting board. Use two forks to shred the chicken.

While the chicken is out of the pot, pour in the half-and-half and stir to combine. Bring the soup back to a gentle simmer over medium-low heat. Do not let it boil.

Add the potato gnocchi to the soup. Cook according to package directions, typically for 3-4 minutes, or until they float to the surface.

Stir the shredded chicken back into the soup. Add the fresh spinach by the handful, stirring until it has wilted completely, which should only take about 1-2 minutes.

Remove the bay leaf. Taste the soup and season generously with salt and freshly ground black pepper as needed.

Ladle the hot soup into bowls. Garnish with grated Parmesan cheese if desired and serve immediately.