Melt butter. Stir in flour - this will thicken into a paste. Stir in milk ... and then grated cheese. Continue stirring; this will take a while to thicken. Stir in spices.
Combine pasta, beef, mushrooms, and cheese sauce in large casserole dish.
Heat through in 350 °F oven, or in microwave.
Notes
This can be a stove-top/microwave meal when the weather is hot.
If you have a soy cheese you like melted, this should work fine with that and with dairy-free margarine and milk. I think it would also work fine with a nutritional yeast-based *cheesish* sauce.
To avoid wheat/gluten, select rice pasta and flour.
Butter and Margarine: Butter is a dairy product made from cow’s milk. Margarine typically contains milk or soy, but there are milk-free and soy-free versions available.
Gluten: Gluten is a protein found in specific grains (wheat, spelt, kamut, barley, rye). Other grains are naturally gluten-free but may have cross-contact with gluten-containing grains. Look for certified gluten-free products if you need to avoid gluten. Find out more about wheat and gluten substitutions.
Milk and Soy Substitutions: Alternative dairy-free milk beverages and products will work in most recipes. Find out more about milk substitutions and soy substitutions.