Preheat oven to 350 degrees.
In a skillet over medium heat, brown chicken lightly in 2 tablespoons butter, add the garlic and mushrooms and keep cooking till chicken mixture is smelling very garlicky.
Transfer browned chicken strips to a baking dish (for your extra casserole, use an aluminum pan that can be tossed after use); arrange artichoke hearts on top.
In the skillet, melt remaining butter and add the flour, whisking to blend (no lumps!). Add broth and cook until thickened then pour over chicken mixture.
Bake the casserole, uncovered, at 350 degrees for about 30 to 45 minutes.