Heat a large Dutch oven or heavy soup pot over medium-high heat. Add the butter and let it melt.
Add the carrots, mushrooms, celery, and shallot or onion. Cook for 3–4 minutes, stirring occasionally, until the mushrooms release their moisture and most of the liquid has evaporated.
Season the vegetables with seasoned salt and black pepper. Reduce the heat slightly if necessary and continue cooking for another 6–7 minutes, or until the vegetables are tender.
Add the minced garlic, poultry seasoning, and dried thyme. Cook for 1–2 minutes, stirring frequently, until fragrant.
Sprinkle the flour evenly over the vegetables. Stir well so the vegetables are coated, then cook for about 1 minute.
Slowly pour in the chicken broth while stirring continuously. This helps create a smooth sauce without flour lumps.
Add the milk and increase the heat to medium-high. Bring the mixture to a gentle simmer, stirring occasionally.
Add the gnocchi and stir to combine. Reduce the heat to medium and simmer for 5–6 minutes, stirring frequently, until the gnocchi are tender and the sauce has thickened.
Stir the shredded chicken and frozen peas into the One Pot Gnocchi Chicken Pot Pie. Cook for another 2–3 minutes, or until the chicken and peas are heated through.
Taste and adjust the seasoned salt and black pepper as needed. Ladle into bowls and serve warm.