Preheat a Dutch oven or another soup pot over medium heat and add about 2 tablespoons of canola oil.
Sear and cook chicken meat until just done and take it out of the pot. Set chicken aside for it to cool down enough for you to handle it.
While chicken is cooking, dice onion, celery, and shred the carrot.
Add another teaspoon of oil into the same pot and add diced onions, celery, and carrots. Cook vegetables until softened.
Dice chicken while vegetables are cooking.
Stir in minced garlic and cook until it's fragrant.
Add chicken back to the pot with vegetables, stir, and pour in chicken stock and milk. Lower the heat to medium low and stir well, scraping the bottom of the pan with a wooden spoon.
Add seasoning and a sprig of thyme.
Optional: Parmesan rind cooked in soup will add great flavor so if you have a whole wedge of parmesan cheese, cut off the rind, and add it to the soup. (You will discard it with the thyme sprig later.)
Cook the soup until it comes to a simmer and them add gnocchi.
Cook just until gnocchi floats or according to the time on package instructions.
Stir in chopped spinach, grated Parmesan cheese, and heavy whipping cream. Cook for a few minutes, until spinach is wilted.
Take off heat right away and discard the sprig of thyme and Parmesan rind.