Over medium heat, heat a 10-inch skillet. Add 2 teaspoons of the oil and 1 ½ teaspoons of the butter and heat until butter melts and foams. Add potato mixture, spreading evenly in the pan, pressing down with a spatula to form a disk. Cook until the bottom is golden brown, about 11 to 12 minutes. Carefully slide the rosti onto a plate, Invert a second plate over the rosti and flip over so that the browned side is now on top. Return skillet to the heat. Add remaining 2 teaspoons oil and 1 1/2 teaspoon butter and heat until melted. Slide the rosti back into the skillet and cook until the second side is golden brown and crisp, about 6 to 7 minutes longer.