Begin by melting the butter in a large deep skillet over medium heat. Add carrots, celery, and onion with a pinch of salt, cooking until they soften (about 6-8 minutes).

Introduce mushrooms and garlic, stirring to cook until mushrooms release moisture and brown (around 5 minutes).

Sprinkle flour over the mixture, stirring to coat evenly; cook for about 2 minutes to eliminate raw flour taste.

Whisk in chicken stock and milk gradually, ensuring no lumps. Stir in mustard, Italian seasoning, and nutmeg, bringing to a simmer.

Fold in the gnocchi, cooking uncovered for 4-5 minutes until they float to the top.

Add cooked chicken and sweet peas, simmering for an additional 3-4 minutes until heated through.

Remove from heat, stirring in parsley and thyme. Adjust seasoning to taste.

Ladle into bowls and garnish with Parmesan if desired. Serve hot.