Preheat the oven to 450 degrees F (230 degrees C). Spray the cups of a 12-cup muffin pan with nonstick cooking spray.
Place 4 to 5 frozen potato nuggets into each muffin cup.
Bake in the preheated oven for 10 minutes.
Remove muffin pan from the oven. Using a small glass (e.g. a small juice glass or shot glass) twist and press the tots downward in each muffin cup to create a potato cup. Return to the oven and bake until deep golden brown, about 15 more minutes.
Remove the pan from the oven and distribute pulled pork evenly between the cups. Add 1 tablespoon of shredded cheese to each potato cup, being careful to try and keep it on top of the pulled pork (not down the sides of the muffin cups).
Return to the oven and bake until the cheese has melted, 4 to 5 minutes. Remove from the oven and transfer the potato cups to a serving platter.
Drizzle with BBQ sauce, add a small dollop of sour cream, and sprinkle with green onions before serving.