In a large pot, heat the olive oil and butter over medium-high heat.
Add the chopped chicken breast to the pot and cook until fully cooked and lightly browned.
Remove the chicken from the pot and set aside.
In the same pot, add minced garlic and diced onion.
Sauté until the onion becomes translucent, about 2-3 minutes.
Add shredded carrots and cook for an additional 2 minutes.
Stir in flour to the pot and mix well with the vegetables.
This will help thicken the soup.
Allow the flour to cook for about 2 minutes.
Gradually pour in the chicken broth while continuously whisking to prevent lumps.
Add the cooked chicken back into the pot.
Add the gnocchi and bring the mixture to a boil.
Reduce the heat to medium-low and pour in the half-and-half.
Add the chopped spinach, thyme, parsley, and nutmeg.
Simmer the soup until the gnocchi is tender, about 5-7 minutes.