If I have fat stalks I peel with a potato peeler before cutting end off and then....
I freeze them. If the stalks are thin and not too tough I freeze as is. Later I pull some out to make asparagus soup or to put in casseroles, pot roast, stir fries, batches of grilled veggies with hot oil to add to a salad, sometimes I saute with other veggies (onions, garlic, mushrooms, red sweet pepper), put in a sauce (usually a reduction of the butter and juices from the veg and half and half) and toss with pasta (I add black olives and fresh herbs) for a quick dinner.
Very versatile the lowly asparagus end.