Put the flour on a deep plate or in a shallow bowl and season well with salt and pepper. Dredge the fish in the flour. Put a large skillet over medium-high heat, add 1 tablespoon oil and 1 tablespoon butter and get the skillet hot. Add the fish and cook until browned on 1 side, 2 to 3 minutes. At the same time, add the prosciutto and cook, stirring, to brown. Then flip the fish, transfer the skillet to the oven and roast until the fish is just cooked through, about 10 minutes.
Remove the fish to 2 plates. Dump the prosciutto out onto paper towels to drain. Put the skillet back over medium heat. Add another tablespoon olive oil, the white wine, half the lemon juice, the capers, the remaining 2 tablespoons butter and the parsley and bring to a boil. Add the asparagus and cook until just tender, about 2 minutes. Season with salt and pepper to taste.
Meanwhile, add arugula to a bowl. Dress with the remaining lemon juice and olive oil to taste. Season with salt and pepper. Shave Parmesan over the arugula and toss lightly.
Pour the sauce over the fish, top with the prosciutto and asparagus and serve with the arugula salad on top. Enjoy!