Preheat the oven to 400 degrees F and place a rack in the middle.
Generously season the New York strip all over with salt and pepper.
Heat a heavy metal roasting pan on the stove over high heat.
Add a film of olive oil. When the oil begins to give off wisps of smoke, carefully put the meat in the pan presentation side down and turn down the heat to medium-high; scatter the trimming scraps around its sides. Sear without disturbing until the meat is evenly browned, about 5 minutes per side. With the meat presentation side up, put the roasting pan in the oven and cook until done medium rare, 140 to 145 degrees F on an instant-read thermometer, about 45 minutes.
Transfer the meat from the roasting pan to a serving platter, cover it with aluminum foil, and let it rest in a warm place for 10 to 15 minutes.
Remove and discard the scraps from the roasting pan and pour off all but a thin film of fat.
Put the pan on the stove over medium-high heat.
Add the shallot and, as soon as it starts to sizzle, pour in the port wine and the stock, stirring and scraping with a wooden spoon to dissolve the pan deposits. With a whisk, stir in the cream. Reduce the heat to maintain a bare simmer and, a piece at a time, whisk in the butter until it melts. Continue cooking until the sauce is thick enough to coat the back of a spoon. Turn off the heat and stir in the mustard and sprinkle with salt and pepper, to taste.
Transfer the sauce to a small saucepan to keep it warm.
Uncover the New York strip and transfer it to a cutting board.
Pour any juices that have collected on the platter into the sauce, stirring it in. With a sharp knife, cut the meat across the grain into slices about 1/2-inch thick, arranging them overlapping on the platter. Ladle a little sauce over the meat and pass the rest alongside.
