Place a large Dutch oven over medium heat and melt the butter with the olive oil.
Add the diced onion, carrots, and celery. Sauté for 5–6 minutes until the vegetables are soft. Add the minced garlic and cook for 1 additional minute.
Sprinkle the flour evenly over the vegetables. Stir constantly with a wooden spoon for 1–2 minutes to create a light roux and cook out the raw flour taste.
Slowly pour in the chicken broth, whisking constantly to prevent any lumps from forming. Bring the broth to a gentle simmer and cook for 5 minutes until it begins to thicken.
Reduce the heat to medium-low. Stir in the heavy cream, dried thyme, salt, and black pepper. Bring back to a very gentle simmer (do not let it rapidly boil!).
Carefully drop in the potato gnocchi and the shredded chicken. Simmer for 4–5 minutes, just until the gnocchi are tender and float to the surface of the soup.
Remove the pot from the heat completely. Immediately stir in the chopped fresh baby spinach. Let the soup sit for 1–2 minutes until the spinach wilts.
Serve hot, garnished with extra cracked black pepper or freshly grated parmesan cheese.