Start with making the sauce, melt butter in a small pot over medium heat until it's foamy, 3-4 minutes.
Place egg yolks and 2 teaspoons of water in blender. Start blending, slowly add hot melted butter until it's all incorporated. Add lemon juice, cayenne, salt and pepper to taste. Transfer to small bowl, place plastic wrap on top of sauce and set aside at room temperature until ready to use.
Toast bread and set aside.
Place butter into non-stick pan and heat on medium to low heat.
Slowly add eggs to skillet. Note: For best results, crack egg into small bowl and add slowly to non-stick pan.
Cover pan with a tight lid and let cook for 2-3 minutes, until the whites are fully set but the yolks are still runny.
Layer avocado mixture onto toast and place egg on top.