Season the scallops on the top with salt and pepper. Melt the butter in a large, deep skillet over medium-high heat. As soon as the butter is melted, place the scallops, seasoned side down in the pan. Sear for 2 minutes until browned on the bottom, and season the top with salt and pepper while they are cooking. Flip the scallops and sear for 2 more minutes; the scallops do not have to be cooked all the way through at this point. Remove the scallops to a cutting board.

Return the skillet to medium heat without cleaning the pan. Add the shallots and cook, stirring, for about 3 minutes until golden brown. Add the white wine and sherry, scraping the bottom of the pan to loosen any browned bits from the bottom. Simmer until the liquid has reduced by half, about 3 minutes. Add the milk and cream to the pan and heat until bubbles form along the edges of the pan.

Meanwhile, cut the scallops into small pieces, about 1/2-inch in size. Add the scallops with any juices that may have accumulated into the pan. Cook for a minute or two until the scallops are heated through.

Ladle the stew into 4 bowls and top each bowl with paprika or cayenne. Add a sprinkle of the chopped parsley if desired.