Spray large pot over medium heat and spray with nonstick cooking spray. Saute onions and carrots with salt and pepper until onions are mostly translucent. Stir in garlic and cook another minute until fragrant.
Add in chicken broth, salt, pepper, tarragon, bay leaves and chicken breasts whole. Cover and bring to boil, then crack the lid and reduce to simmer until chicken breasts are thoroughly cooked. (Depending how thick your chicken breasts are, this can take anywhere between 15-30 minutes.)
While chicken is cooking, whisk evaporated milk with flour until smooth.
Once chicken is finished cooking, remove from pot and shred. Replace back into pot. Add gnocchi and evaporated milk-flour mixture and bring to a simmer. Stir constantly while it is thickening and then reduce heat to low once it has thickened completely-this process should take 5 minutes. The soup should have thickened and the gnocchi should be floating and finished cooking. Taste and add more salt and pepper if necessary. (I made this three times and always added more salt and pepper since the evaporated milk has no seasonings.) Remove bay leaves. Stir in spinach and heavy cream right before serving.
Divide equally between 8 bowls and serve hot.
Notes
The more accurate macros for 1 serving (1/8th) of this recipe: 299 calories, 4.4g F/34.1g C/23.2g P.