Preheat the oven to 425F. Grease a 9-inch spring form pan with butter.
Make the potato crust. Add the potatoes to a large pot, add a generous pinch of salt, and enough water to cover the potatoes. Bring the water to a boil. Boil until the potatoes are fork-tender, about 15-20 minutes.
Strain the potatoes and let them air-dry for about 5 minutes, then add them to the spring form pan. Use the bottom of a jar to smash the potatoes and then use your hands to spread the mashed potato so that it covers the base and the sides of the pan.
Brush the crust with olive oil, season with salt and pepper, then sprinkle a layer of grated Parmigiano Reggiano over the crust.
Bake on the top rack of your oven for 25 minutes. Remove from oven and set aside.
Lower the oven to 375F.
Caramelize the onions. Add 1 tablespoon butter to a large skillet and heat over medium-high. Add the onions and salt. Cook for 8 minutes on medium-high, stir occasionally, then reduce the heat to medium-low and continue to cook until the onions are a golden brown.
Make the compound butter. Add all the compound butter ingredients to a bowl and use a spoon to mash and combine. Set aside
Cook the Steak. Preheat your grill to high. Season the steak generously with salt and pepper. Grill for 4-5 minutes on each side. Let the steak rest for 10 minutes and then slice the steak into 1-inch cubes.
Fill the potato crust with layers of onion, steak, dollops of compound butter, and cheese. Finish with a layer of cheese. Bake for 15 minutes or until the cheese has melted.
Let rest for 5 minutes, then cut and serve warm!