Cook the chicken breasts by poaching in broth, baking at 400°F for 20 minutes, or using leftover rotisserie chicken. Shred the chicken with two forks and set aside.
Melt butter in a large Dutch oven or heavy-bottomed pot over medium heat. Add diced onion, carrots, and celery. Cook for 5 to 6 minutes until vegetables soften and onion turns translucent.
Add minced garlic and dried thyme. Stir for 30 seconds until fragrant.
Sprinkle flour over the vegetables and stir constantly for 1 minute to cook out the raw flour taste and create a roux.
Slowly pour in chicken broth one cup at a time, whisking continuously to prevent lumps. Stir in heavy cream.
Bring the mixture to a gentle boil then reduce heat to medium-low. Simmer for 10 minutes until the soup thickens.
Drop the gnocchi directly into the simmering soup. Cook for 3 to 4 minutes until gnocchi float to the surface.
Stir in the shredded chicken and heat through for 2 minutes.
Remove the pot from heat and stir in fresh baby spinach until just wilted. Season with salt, pepper, and a pinch of nutmeg if desired.
Ladle into bowls and serve immediately. Enjoy with crusty bread on the side.
