Over medium heat, melt butter in a large stew pot.
Stir the melted butter into the flour until a smooth consistency is reached.
Stir continuously while adding the chicken broth gradually until no lumps are visible.
Add shredded chicken, black pepper, salt, Italian dressing mix, and garlic powder.
Bring the mixture all the way up to a boil.
Turn the heat down to a simmer and cook for about 12 to 15 minutes.
Add milk, white wine, lemon juice, and chopped parsley.
Turn the heat down to low.
Add the cooked rice, and cover the pot with its lid.
Cook the rice until it is heated up through.
Serve in a soup bowl and enjoy!