Whisk egg yolks, water, and lemon juice together in a small saucepot. Begin heating the ingredients at very low heat while continually whisking them. Don’t stop whisking as the egg yolks begin to thicken in the pot.
Once the egg yolks have thickened, keep whisking while you add 1 tablespoon of butter to the pot. Once the butter melts into the eggs, add another tablespoon. Keep adding a tablespoon of butter at a time, whisking each one in, until all the butter is used up. Season the hollandaise sauce with salt and paprika.
Leave the hollandaise sauce aside to cool and thicken. Prepare the avocado by slicing one in half and scooping out a spoonful of fruit from each half. Slice the avocado fruit you scoop out and reserve it for serving.
Bring a new pot of water to a boil, and poach one egg for each half avocado. If you need advice on how to poach an egg, refer to the introduction at the beginning of the recipe. Ladle each poached egg into an avocado half.
Salt your poached egg and avocado to taste. Spoon the hollandaise sauce over the poached eggs and the sliced avocado from step 3. There will likely be extra sauce for eating with the eggs. You can serve with extra paprika or some chopped parsley.