Melt the butter in a large frying pan and add the chicken.
Cook the chicken on both sides until lightly browned, then add the mushrooms and onions.
Saute until the mushrooms and onions are softened and have released their liquid. Add the water. Scrape the browned bits off the bottom of the pan and toss in a bay leaf and some salt.
Cover with a lid and simmer on low for 30 - 45 minutes until reduced and the liquid has taken on the flavor of the ingredients. Then, remove the chicken and bay leaf.
Boil the water and cook pasta according to package directions. Cut the chicken and return it to the pan, discarding the bones.
Mix the milk and flour. I usually use whole wheat flour, but sometimes arrowroot. Depending on how thick you like your sauce, you may need more flour (not arrowroot; never more than 1 tablespoon per cup of liquid).
Add the milk mix to the pan and stir until smooth and thickened. Add the cheese and stir until melted. Serve over pasta.