Preheat the oven to 400 degrees. Bring a large pot of water along with the vinegar to a boil over a high flame. In a small saucepan over a low flame, melt the butter. Add the chopped herbs along with a pinch of salt and pepper and stir for 1 minute, until bubbly. Remove from the heat and set aside. In a large bowl, toss the asparagus with the oil along with a pinch of salt and pepper. Spread in an even layer on a lightly oiled baking sheet. Place in the oven and roast until slightly browned, turning once, about 10-12 minutes. Meanwhile, lay the slices of bread on a separate baking sheet and in the oven for 2-4 minutes, turning once, until slightly toasted on each side. Set aside.
When the water is fully boiling, reduce the flame to medium-low. Using a wooden spoon, carefully stir the water to create a vortex. Crack an egg into a small bowl, making sure not to break the yolk. Pour into the center of the simmering water. Repeat with the remaining eggs. Continue to simmer until the whites are completely opaque and the yolks are slightly firm, about 4 minutes for medium. Remove gently to a bowl with a slotted spoon.
Spread a small amount of the herb butter on each piece of toast. Divide evenly between 2 plates. Top each toast with a poached egg, asparagus and radish. Season with a pinch of salt and pepper to taste.