Melt butter in a medium-sized saucepan. Add in the chopped onion, garlic, and mushrooms and cook until the onion is translucent, 2-4 minutes.
Whisk in the flour and cook for 30 seconds. Add in the half and half, stirring so that no flour clumps remain. Bring to a soft boil, then reduce the heat and let simmer for 5-8 minutes, stirring occasionally.
Add in the Italian seasoning, cheese, and salt and pepper to taste.
Add in the artichoke, spinach, and cooked chicken, stirring to combine. Serve over cooked pasta!