Fill a pan half way full of water. Bring to a boil and stir in the bouillon cube until dissolved. Crack one egg into a measuring cup or large spoon and gently slip it into the boiling water. Repeat with remaining eggs. Simmer for about 5 minutes over medium heat. Remove with a slotted spoon (the kind used for deep frying pooriyan) and keep warm.
Meanwhile, place the asparagus into a wide pan and fill with enough water to cover. Bring to a boil, and cook until asparagus is tender, about 4 minutes. Drain.
Toast the bread to your desired darkness. Spread butter onto each piece of toast. Top with a slice of cheese, then a poached egg and finally, asparagus. Season with salt and pepper and serve immediately.