Glazed Cooked and Raw Asparagus with Butter and Parmesan

To cook the asparagus: Using kitchen string, tie the asparagus spears together in bunches of five.
Bring a large pot of water, with the salt, to a rapid boil.
Plunge in the asparagus bunches and cook until the tip of a knife can pierce a stalk without resistance, about 4 minutes.
Remove the asparagus and pat the bunches dry, then carefully untie the strings.
Melt 3 tablespoons of butter in each of two large skillets over medium heat (if you have just one large frying pan, cook in two batches).
When the butter is white and bubbly, lay the asparagus in the pans in a single layer.
Roll the stalks around so that each gets well covered with butter and cook for 2 minutes or so, until they take on a shiny, "gilded" look.
Sprinkle on the Parmesan and remove from the heat.
To finish the dish: Divide the asparagus among four warmed serving dishes, then scatter the chopped asparagus tips over the cooked asparagus.
Sprinkle a pinch of freshly ground pepper over each serving, then drizzle 1 teaspoon of chilled olive oil in a thin filament around the edge of each plate.
Serve immediately.
Variations: Instead of drizzling olive oil onto the serving plates, substitute a thin filament of highly reduced pan drippings from a roast, punctuated around each plate by 6 tiny Nicoise olives.
Or garnish each plate with 4 fresh morel mushrooms that have been sauteed in butter with minced shallots.