Melt the fat of your choice in a skillet. Add the thinly sliced mushrooms and 1/4t of salt to the hot oil and cook until browned on both sides.
Remove the mushrooms and add the asparagus and remaining salt to the pan. Stir the asparagus around so that each spear is coated in fat. Add water to the pan to steam the asparagus and cover with a lid.
Remove the lid periodically to stir the asparagus. You are aiming for bright green and tender stalks that aren't mushy and complete evaporation of the water added to the pan. When the stalks are bright green there shouldn't be much water remaining. If there is a bit you can remove the lid to let it evaporate if the asparagus is nearly cooked. If the asparagus is completely cooked simply remove it from the pan and don't worry about the water. We don't want to overcook your asparagus.
Top the asparagus with the cooked mushrooms.