In large skillet, heat 2 tablespoons olive oil over medium-low heat. Add garlic; sauté 1 minute or until very lightly browned. Remove garlic with slotted spoon; reserve for later use. Add asparagus and broth to hot oil; simmer 3 minutes or until crisp-tender, turning asparagus occasionally. Season with salt and pepper to taste.
Fill a large pot halfway with water. Add white vinegar and salt. Bring to a boil over high heat; reduce heat to low. Break eggs into custard cups, one at a time. Gently slide eggs into hot water, in 2 to 3 batches. Poach eggs 3 to 4 minutes or until egg whites are firm and yolks are slightly thickened. Remove eggs with slotted spoon.
Place toast on 4 serving plates. Top each evenly with Serrano ham, asparagus spears, asparagus broth and 2 poached eggs. Sprinkle with cheese, parsley and reserved garlic. Drizzle plates evenly with remaining 2 tablespoon olive oil. Sprinkle lightly with paprika.