Heat the oven to 375 degrees F and grease a 9x13 inch baking dish. The dish should be ready before the filling is mixed so the potatoes can go in while the mixture is still warm and easy to spread.

If you are using baking potatoes or russets, peel them and cut them into 1/2-inch pieces. Keep the pieces fairly even so they cook at the same rate and finish with a consistent bite.

Place the cut potatoes in a medium saucepan, cover with cold salted water by about 1 inch, and bring to a boil before reducing to a gentle boil for 12 to 14 minutes. Drain when the potatoes are fork tender with a little resistance left in the center, then let them cool slightly so they do not break apart in the bowl.

Whisk the melted butter, sour cream, condensed soup, and green onion together in a medium bowl, then stir in 1 1/2 cups cheese and the slightly cooled potatoes. The mixture should look thick, creamy, and evenly combined, with no separate streaks of sour cream or soup left behind.

Spoon the warm potato mixture into the prepared baking dish and spread it into an even layer. An even layer helps the casserole heat through evenly and brown across the top instead of just around the edges.

Scatter the remaining 1/2 cup cheese over the top and bake for 28 to 30 minutes. Pull it when the edges are bubbling and the top is browned in spots with melted cheese across the surface.