Heat vegetable oil in a large skillet over medium-high. Add pork and cook, undisturbed, until browned underneath, about 2 minutes. Break up with a wooden spoon or a spatula and continue to cook, stirring and breaking into large pieces, until browned all over but still pink in places, about 2 minutes more. Add rice cakes, ginger, garlic, and half of scallions; season with salt and plenty of pepper. Cook, stirring occasionally, until pork is cooked through and rice cakes are browned in spots, about 4 minutes. If pan looks a bit dry at any point, pour in a little more oil. Remove pan from heat; add butter, soy sauce, and sesame oil and toss to coat.