In a large Dutch oven or oven-safe skillet, melt the butter over medium heat. Add the diced onion, carrots, and celery. Cook until they begin to soften, about 5-7 minutes. Stir in the minced garlic and cook for another minute until fragrant.

Sprinkle the all-purpose flour over the cooked vegetables. Stir constantly for about one minute to cook out the raw flour taste.

Gradually whisk in the chicken broth, ensuring there are no lumps. Slowly pour in the heavy cream, stirring until the mixture is smooth.

Bring the sauce to a gentle simmer. Stir in the dried thyme, salt, and black pepper. Let it cook for about 5 minutes, allowing the sauce to thicken slightly.

Stir the cooked, shredded chicken and the uncooked gnocchi directly into the simmering sauce. Ensure the gnocchi is mostly submerged.

Reduce the heat to medium-low, cover, and let it cook for 5-7 minutes, or until the gnocchi is tender and cooked through. Remove from the heat, stir in the frozen peas and fresh parsley. Let it sit for a few minutes before serving.