Warm the olive oil in a large pot over medium heat.
Add the celery, onion, garlic, and shredded carrots to the pot and cook, stirring occasionally, until the onions become translucent, about 2 to 3 minutes.
Pour in the cooked chicken pieces, chicken broth, thyme, and season with salt and pepper.
Bring the mixture up to a boil, then add the potato gnocchi gently stirring to combine.
Allow it to boil for 3 to 4 minutes until the gnocchi begin to float.
Lower the heat to a simmer and let the soup cook for an additional 10 minutes.
Mix in the half and half and the chopped spinach, cooking for another 1 to 2 minutes until the spinach softens.
Taste the soup and adjust salt and pepper as needed before serving.