Thinly slice chicken breasts and season with salt and pepper. Heat vegetable oil in a skillet and cook chicken breasts until cooked through. Shred after cooled
While chicken is cooking, add butter to a Dutch oven over medium heat. Add carrots, celery, and shallots. Season with salt and pepper and stir, cooking for about 10 minutes
Add garlic and dried thyme, then saute for another 1-2 minutes
Sprinkle flour over vegetables and stir to combine, then cook for a minute. Slowly pour in chicken broth while stirring, then add milk. Turn up heat until mixture comes to a bubble, stirring occasionally. Add gnocchi and stir. Turn down heat to medium and simmer, stirring frequently, until gnocchi are tender, about 6 minutes
Stir in chicken and peas. Taste and season with salt and pepper. Ladle into bowls and serve