Heat the oil in a large skillet over high heat until shimmering. Add the onion and cook until slightly softened, about 4 minutes, then add the ground beef and 1 1/2 teaspoons salt. Cook, breaking up clumps with a wooden spoon, until brown, about 8 minutes. Reduce the heat to medium-high and add the allspice, nutmeg and white pepper. Sprinkle the flour on top and stir until incorporated. Stir in the heavy cream and beef broth and bring to a simmer. Add the peas and carrots and parsley.
Pour the mixture into a 9-by-13-inch baking dish. Sprinkle 1 cup cheese evenly on top. Top with the potato tots and sprinkle the remaining 1/2 cup cheese on top.
Bake until the potato tots are golden brown, about 40 minutes. Cool 10 minutes before serving.