1. Combine first 6 ingredients in a large bowl, stirring with a whisk. Using a sharp peeler, thinly peel asparagus to equal 3 cups asparagus ribbons. Add asparagus and parsley to bowl; toss gently to coat.
2. Combine 8 cups water and white vinegar in a large skillet; bring to a simmer. Break each egg into a custard cup, and pour each gently into pan. Cook 3 minutes or until desired degree of doneness. Remove eggs from pan using a slotted spoon.
3. Place about 2/3 cup asparagus mixture on each of 4 plates. Sprinkle each serving with 1 1/2 teaspoons almonds; top each serving with 1 egg. Sprinkle evenly with Manchego cheese.