For the hollandaise sauce: Place the yolks, lemon juice and water into a blender and blend for 1 minute. With the blender running, pour the butter through open hole of the blender lid. Season with salt and pour into the top of a double boiler set over hot water to keep warm.
For the toast: Toast the bread until golden, then spread with 1 tablespoon butter. Divide the bread among 4 plates, butter-side up, and spread some of the radishes evenly over them (reserve some radishes for topping). Lay an avocado half on a cutting board cut-side down and slice thinly, crosswise (thinner slices are easier to roll). Put the flat side of your knife along the side of the avocado. Press the knife against the slices and they will fan out, overlapping each other. Starting from the thin end, curl the avocado slices into a cylinder toward the center. Continue curling the avocado slices until you get a 3- to 4-inch circle that looks like a rose. Repeat with the remaining avocado halves; set aside.
Heat the remaining tablespoon butter in a large nonstick skillet over medium heat. Crack the eggs into the skillet and cook until the whites have set and the yolks are still runny. Put 1 egg on each toast, top with the avocado flowers, using a spatula to transfer each to a toast, and garnish with the sliced radishes and sprigs of dill or cilantro. Sprinkle with coarse salt. Serve with the hollandaise sauce on the side.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
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