Cook onions, celery, carrots, in microwave for 3 minutes, to soften a little.
Melt 2 tablespoons butter in a nonstick pan over medium-high heat. Stir in soften vegetables. Add thyme and a pinch each of salt and pepper. Cook, stirring, until the vegetables are soft, about 5 minutes. Add chicken broth and ¾ cup water and bring to a boil. Stir in gnocchi, breaking apart any that are sticking together. Cover and simmer until gnocchi is just tender, about 5 minutes.
Uncover pan and stir in cooked chicken, peas, and milk. Cook until slightly thickened, about 2 minutes; season with more salt and pepper, if desired.