1. Adjust oven rack to uppermost position and heat broiler (about 4 inches from the heating element). Toss asparagus with oil and salt and pepper, then lay spears in single layer on heavy rimmed baking sheet. Broil, shaking the pan halfway through to turn spears, until asparagus are tender and lightly browned, 6 to 10 minutes.

2. Bring the vinegar to a boil in an 8-inch skillet over medium-high heat. Reduce the heat to medium and simmer slowly until the vinegar is syrupy and reduced to 1/4 cup, 15 to 20 minutes. Arrange the broiled asparagus on a serving platter. Drizzle the balsamic glaze and olive oil over the asparagus. Sprinkle with the Parmesan and serve immediately.

SNAPPING OFF THE TOUGH ENDS: Hold the asparagus about halfway down the stalk; with the other hand, hold the cut end between the thumb and index finger about an inch or so up from the bottom and bend the stalk until it snaps.