Preparation Line large bowl with kitchen towel. Coarsely grate potatoes into towel. Enclose potatoes in towel and squeeze out as much moisture as possible. Heat 1 1/2 tablespoons oil in nonstick skillet over medium heat. Using metal spatula, press half of potatoes over bottom of skillet in even layer. Sprinkle with coarse salt and pepper. Leaving 1/2 inch plain border, sprinkle cheese and white parts of onions over potatoes. Press remaining potatoes over filling in even layer. Cook until crisp and golden on bottom, pressing occasionally with spatula, about 10 minutes. Place rimless baking sheet over skillet and invert galette onto sheet. Add 1 1/2 tablespoons oil to same skillet. Slide galette, browned side up, into skillet. Cook until crisp and golden on second side, about 10 minutes longer. (Can be made 2 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 green parts of onions.
Preparation Line large bowl with kitchen towel. Coarsely grate potatoes into towel. Enclose potatoes in towel and squeeze out as much moisture as possible. Heat 1 1/2 tablespoons oil in nonstick skillet over medium heat. Using metal spatula, press half of potatoes over bottom of skillet in even layer. Sprinkle with coarse salt and pepper. Leaving 1/2 inch plain border, sprinkle cheese and white parts of onions over potatoes. Press remaining potatoes over filling in even layer. Cook until crisp and golden on bottom, pressing occasionally with spatula, about 10 minutes. Place rimless baking sheet over skillet and invert galette onto sheet. Add 1 1/2 tablespoons oil to same skillet. Slide galette, browned side up, into skillet. Cook until crisp and golden on second side, about 10 minutes longer. (Can be made 2 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 green parts of onions.