Coarsely grate potatoes in a food processor. Line a large bowl with a kitchen towel. Add grated potatoes; squeeze out as much moisture as possible.

Heat 1½ Tablespoons vegetable oil in a non-stick 9-inch skillet over medium heat. Using a metal spatula, press half of potatoes into the skillet in an even layer. Sprinkle with chopped onion, shredded cheese, salt and pepper. Press remaining potatoes over filling in even layer, being careful to completely cover the filling.

Cook over medium heat until crisp and golden on bottom, pressing occasionally with spatula, 10 to 15 minutes. Gently loosen bottom of galette with a spatula. Place rimless baking sheet over skillet and invert galette onto baking sheet. Add 1½ Tablespoons oil to the same skillet. Slide galette, browned side up, into skillet. Cook until crisp and golden on second side, 10 to 15 minutes. (Can be made two hours ahead. Turn out onto baking sheet. Let stand at room temperature. Rewarm on sheet in 350° F oven until crisp, about 15 minutes). Transfer to platter. Cut into 8 wedges. Top with chopped green onion. Yield: 6 to 8 servings.