To the pitcher of your blender, add the avocado, dijon mustard, lemon zest, lemon juice, oil, water, parmesan cheese, and a dash of salt and black pepper. Blend until completely smooth. If you would like a thinner consistency, add more water as needed. Season to taste with salt and black pepper, cover, and refrigerate until you are ready to serve.
To a large nonstick skillet, add the oil and heat over medium-high heat. Season the ribeye generously with salt and black pepper and place it on the hot pan. Cook for about 2-3 minutes per side, for blue or rare. You may cook it longer based on your liking. Remove from heat and let stand for about 5 minutes. Keep the heat on and add another tablespoon of oil if there is none left in the pan. At this point, you may refrigerate it until you are ready to serve or slice it thinly immediately.
To the pan now add the sliced bread in batches. Toast on both sides until browned to your liking and then carefully remove from pan.
Assemble your open-faced steak sandwiches by spreading a thin layer of parmesan avocado cream. On top of the cream, add the arugula and then the steak. Top with sliced radishes and a drizzle of cream. Season with black pepper and enjoy immediately!