In a heavy medium saute pan, melt 2 tablespoons of the butter with 1 tablespoon of the olive oil over medium heat. Spread the potatoes in an even layer in the saute pan, pressing down on them slightly with a spatula. Season with salt and pepper and cook until the potatoes begin to brown on the bottom, 6 to 7 minutes, shaking the pan occasionally to prevent sticking. Pour 1 tablespoon of the melted butter over the top of the potatoes.
Place a large plate over the pan and invert the potatoes onto the plate. Add the remaining 2 tablespoons butter and 1 tablespoon olive oil to the pan, slide the potatoes back in, and brown on the other side, about 5 minutes more. Season with salt and pepper and slide onto a platter. Serve immediately.