1. Heat 1 tablespoon oil in 12-inch skillet over medium-high heat until shimmering. Add onion and cook, stirring occasionally, until softened and lightly brown, 4 to 5 minutes. Transfer onion to bowl and cover with foil. Rinse out pan with water and dry well with paper towels.

2. While onion cooks, combine 1 tablespoon oil, eggs, capers, and vinegar in medium bowl. Season with salt and pepper to taste; set aside.

3. Return skillet to medium-high heat; add remaining tablespoon oil and butter. When butter has melted, add half of asparagus to skillet with tips pointed in one direction; add remaining spears with tips pointed in opposite direction. Using tongs, distribute spears evenly (spears will not quite fit into single layer); cover and cook until asparagus is bright green and still crisp, about 5 minutes.

4. Uncover and increase heat to high; season asparagus with salt and pepper. Cook until spears are tender and well browned along one side, 5 to 7 minutes, using tongs to occasionally move spears from center of pan to edge of pan to ensure all are browned. Transfer asparagus to serving dish, top with onions. Adjust seasonings with salt and pepper; sprinkle with egg mixture, and if desired, squeeze lemon over spears. Serve immediately. To Serve 2-3: Cut all ingredient amounts in half. Cook asparagus in 10-inch skillet over medium heat, covered, for 3 minutes. Remove cover and cook over medium-high heat until tender and browned, 3 to 4 minutes. Do not adjust heat when cooking garnishes; however, cooking times for garnishes should be reduced by 1 to 2 minutes.

Serves 4 to 6