One at a time, place the veal medallions between 2 sheets of plastic wrap and pound with the flat side of a meat mallet until 1/8-inch thick. Season the veal on both sides with 1 teaspoon each of the salt and pepper. Place the flour in a shallow dish. One at a time, dredge the veal medallions in the flour, and shake to remove any excess.
Heat 3 tablespoons of the oil in a large skillet over medium-high heat. Add 3 or 4 of the medallions and cook until golden, about 1 minute per side. Remove from the pan. Cook the remaining medallions, adding more oil as needed.
Discard any oil remaining in the pan, and melt 2 tablespoons of the butter over medium-high heat. Add the mushrooms and green onions and cook, stirring, until wilted, 3 to 5 minutes. Add the crabmeat and the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Cook, stirring gently, until warmed through, about 1 minute.
Meanwhile, in a large skillet, melt the remaining 1 teaspoon butter over medium-high heat. Add the asparagus and toss until heated through, about 1 minute.
To serve, shingle 3 medallions alternately with the crabmeat mixture on each of 4 plates. Top each serving with 4 asparagus spears and drizzle with the hollandaise sauce. Serve immediately.
In the top of a double boiler or in a large heatproof bowl set over a pot of simmering water, whisk the egg yolks with the water until thick and pale yellow, removing the pan or bowl from the heat as needed to prevent the eggs from overcooking. Gradually add the butter, whisking constantly until thickened. Add the remaining ingredients and whisk well to blend. Adjust the seasoning, to taste.
Remove from the heat and cover to keep warm until ready to serve. (Or, place in a bowl set over a pot of warm water and cover; stir occasionally.)
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.