Peel and cut potatoes into 1/2-inch cubes, then place in a bowl of cold water to prevent browning. Shred the zucchinis using a box grater or food processor, then wrap them tightly in a clean kitchen towel and squeeze firmly to remove excess moisture—this is crucial for preventing a watery casserole. Preheat your oven to 350°F while you prepare the remaining ingredients.
Melt 1/4 cup butter in a large skillet over medium heat, then add the sliced green onions and cook for about 2 minutes until fragrant and slightly softened. Pour in the sour cream and cheese sauce, stirring constantly until the mixture begins to bubble. Add the shredded cheddar cheese and stir until completely melted and smooth—the sauce should be creamy and cohesive at this point.
Drain the potatoes from their cold water and pat them dry with paper towels to remove excess moisture. Fold the drained potatoes and squeezed zucchini from Step 1 into the cheese sauce from Step 2, stirring gently but thoroughly until all vegetables are evenly coated. Pour the mixture into a 9x13 inch baking dish, spreading it into an even layer. I like to do a quick taste test of the sauce mixture at this point and add a pinch of salt if needed, since the vegetables will release some liquid as they cook.
In a small bowl, combine the melted butter with the Panko bread crumbs, garlic powder, and smoked paprika, mixing until the breadcrumbs are evenly coated and have a slightly damp texture. Sprinkle this mixture evenly over the top of the casserole, pressing it gently so it adheres to the surface—this creates a delicious golden crust as it bakes.
Bake in the preheated 350°F oven for 45-50 minutes until the top is golden brown and the edges are bubbling slightly. The casserole will be piping hot, so let it rest for at least 10 minutes before serving—I find this helps the casserole set up and makes it easier to cut into clean portions. You can serve it warm or at room temperature depending on your preference.