Fill a large saucepan two-thirds of the way with water. Add the white vinegar and bring to a boil.
Holding the tip and stem of each asparagus spear, snap the asparagus where it will naturally break. Discard the ends. Toss the asparagus with about 1 tablespoon olive oil and some salt.
Place the asparagus in the oven and roast for 15 minutes.
Reduce the heat on the water until the bubbles in the water have subsided.
Gently crack and drop the eggs into the water. Cook the eggs for 3 to 4 minutes. When done, the whites will be cooked through and the yolks will be warm but still liquid.
Using a slotted spoon, carefully remove the eggs from the saucepan and blot the bottom of the spoon on a paper towel before plating the egg.
Remove the asparagus from the oven.
Divide the roasted asparagus spears on plates and top each set of asparagus with a poached egg. Sprinkle with the grated Parmigiano and a couple flakes crushed red pepper. Sprinkle with a few drops olive oil.