In a small bowl, combine butter, parsley, tarragon, lemon juice and peel and a dash of salt; chill until serving.
In a large saucepan, place steamer basket over 1 inch of water. Place asparagus in basket. Bring water to a boil. Reduce heat to maintain a simmer; steam, covered, 3-4 minutes or until crisp-tender.
Meanwhile, place 2-3 inches of water in a large skillet with high sides; add vinegar. Bring to a boil; adjust heat to maintain a gentle simmer. Break cold eggs, one at a time, into a custard cup or saucer, holding cup close to surface of water, slip eggs into water.
Cook, uncovered, 3-5 minutes or until whites are completely set and yolks begin to thicken but are not hard. Using a slotted spoon, lift eggs out of water.
Spread 1-1/2 tsp. lemon butter over each English muffin half; top with 4 asparagus spears, 1 egg and another 1-1/2 tsp. lemon butter. Sprinkle with pepper and remaining salt.