Prepare an ice bath and set aside. In a medium saucepan over high heat, add the water, 1 teaspoon of the salt, the white vinegar and the eggs. Bring to a boil, then remove from the heat and let stand for 4 minutes. Shock the eggs in the ice water bath. Once the eggs are cool, peel and set aside.
In a medium bowl, smash the eggs into small pieces using the back of a fork, then stir in ¼ cup of the olive oil, red wine vinegar, chorizo, shallot, pepper and the remaining salt until well incorporated.
Heat a grill pan over medium-high heat. Toss the asparagus with the remaining 2 tablespoons olive oil and grill until cooked through and slightly charred, about 2 to 3 minutes on each side. Serve warm with the egg mixture spooned over the top.