Preheat oven to 400°F. On a baking sheet with rim, toss asparagus with oil. Season with salt. Bake until asparagus is lightly browned and tender, approximately 15-18 minutes.

In a small saucepan, cook balsamic vinegar and brown sugar over medium-high heat until syrupy and reduced to 3 tablespoons. approximately 6 minutes

Meanwhile, bring a large skillet with 2 inches of water to a simmer over medium heat. Add cider vinegar and season with salt. Break one egg at a time into a cup, then tip cup into pan. Simmer until whites are set and yolks are slightly set, about 3 minutes. With a slotted spatula, scoop out eggs one at a time and drain on paper towels. Trim edges with a paring knife, if desired.

Divide asparagus among four plates and drizzle with reduced balsamic. Top with shaved Parmesan and an egg