To a Dutch oven or large pot, heat the olive oil over medium-high. Add the chicken and 1/2 teaspoon salt. Sauté until the chicken is golden brown and cooked through, about 4-5 minutes. Remove to a plate and set aside.
Reduce the heat to medium and add the butter. As soon as it is melted, add the carrots, celery, and onion. Sauté until the onion is softened, about 5 minutes, adjusting the heat as needed so that it turns translucent but does not brown.
Stir in the Italian seasoning, celery salt, pepper, and garlic until combined.
Splash two tablespoons of evaporated milk into a small bowl or cup. Add the cornstarch and whisk to form a cornstarch slurry.
Add the cornstarch slurry, remaining evaporated milk, and chicken broth. Bring the liquid to a boil for a brief second (necessary for thickening), then reduce heat, partially cover the pot, and let simmer for 10 minutes to thicken.
Stir in the gnocchi and cauliflower. Continue to simmer with the pot partially covered, until the gnocchi is tender and cooked through, about 8 to 10 minutes.
Remove the pot from heat and stir in the chicken and spinach.
Taste check and add additional salt, pepper, or seasonings as needed.
Serve hot with a sprinkle of parmesan, parsley, and a few cracks of black pepper.