Melt the butter in a small saucepan. Be sure the butter does not get so hot that it starts turning brown!
In a separate small bowl, beat the egg yolks. Add the lime juice, whipping cream, and salt and pepper. Add a small spoonful of the melted butter to the egg mixture and stir well. Repeat this process adding a spoonful at a time of hot butter to the egg mixture.( Adding the butter slowly, a spoonful at a time, will ensure that the egg mixture does not start to curdle).
For the eggs
To poach the eggs, first fill a medium size pot with about 3 inches of water. Heat the water on high heat until it starts to steam and bubble, just before boiling point. If the water is boiling it is too hot!
Crack one egg into a small dish or cup. Add a splash of white vinegar to the pot of water. Use a large slotted spoon to swirl the water in the pot to create a gentle whirlpool. Carefully pour the egg into the center swirl of the water.
Once the egg is cooking in the water, make sure to watch the water temperature so that the water never begins to boil. (Oftentimes this means adjusting the water to medium heat so that the water stays just below boiling point). The cooking time will depend on how well done you want the yolk of the egg to be. I like to cook the egg for about 5 minutes, which yields a soft yolk.
In the meantime, you can cook your asparagus. Fill a large skillet with about 1 inch of water. Bring to a simmering boil and add the asparagus spears. Cook for just a few minutes, until tender. Remove to a paper towel.
Slice the English muffins in half and toast them. Add a tomato slice to each half, followed by a piece of bacon and 2-3 asparagus spears.
Once the egg is done cooking, remove it from the water with a large slotted spoon and place it on top of the asparagus.