How to Make It
Bring the water to a boil in a medium saucepan; cover and keep warm over low heat. Melt the butter in a large saucepan, add the onion and cook over low heat, stirring, until translucent, about 8 minutes.
Add the barley to the onion and cook over moderate heat, stirring, until thoroughly coated with butter, about 2 minutes. Add 2 cups of the hot water and simmer, stirring often, until the water has evaporated, about 10 minutes. Repeat the process with the remaining water, adding 2 cups at a time. Remove the barley from the heat. Stir in 1 cup of the Parmesan and season with salt and pepper. Spread the barley on a baking sheet, cover with plastic and let cool.
Line a 10-inch cake pan with plastic wrap, allowing a 6-inch overhang. Using a rubber spatula, spread half of the barley evenly in the cake pan. Sprinkle with the remaining 1/2 cup of Parmesan and cover with the remaining barley; smooth the surface. Cover the barley cake with the overhanging plastic wrap and refrigerate until firm, at least 4 hours or overnight.
Heat the oil in a 10-inch nonstick skillet. Working quickly, unwrap the barley cake and gently lift it from the pan using the plastic wrap. Invert the cake onto an unrimmed baking sheet, discard the plastic wrap and slide the cake into the skillet. Cook over moderate heat until the cake is heated through and very brown and crisp on the bottom, about 15 minutes. Set a large serving plate over the skillet, invert the cake onto it and serve cut into wedges.