Wrapping roe with prosciutto protects its delicate membrane from direct heat.
Preheat oven to 400°. Rinse the roe in cold water; pat dry. Carefully separate each pair of roe into two lobes. Season with pepper. Lay out 2 slices of prosciutto with the long sides overlapping about ½ inch. Place one piece of roe across the slices at one end, then roll it up snugly in prosciutto so that the roe is completely concealed. Repeat with the other three pieces of roe.
In a large nonstick skillet over medium heat, melt 1 tablespoon butter until foamy and add the roe bundles, seam side up. Cook gently about 1 minute, then turn each piece. Place pan in oven and cook until done, about 8 to 10 minutes or when internal temperature reaches 135°. Drain roe bundles on paper towels; keep warm. Reserve the drippings.
In a heavy Dutch oven or other large pan, melt the remaining 2 tablespoons butter over medium heat and add shallot and garlic. Cook, stirring 1 minute, then add the greens and scallions. Continue to stir as greens wilt, about 3 minutes. Stir in lemon juice and drippings, then adjust seasoning with salt and pepper if necessary.
To serve, slice the roe crosswise into ½-inch disks with a very sharp knife, then arrange around the braised greens. Serve with warm crusty bread.