How to Make It
In a large saucepan, melt 2 tablespoons of the butter. Add the shallots and cook over high heat, stirring, until softened, 2 minutes. Add the couscous and cook, stirring, for 2 minutes. Remove from the heat. Add the broth and a pinch of salt, cover and let stand for 5 minutes, until the liquid has been absorbed.
Fluff the couscous and scrape it into a large bowl. Let cool for 5 minutes, stirring occasionally. Stir in the eggs and cheese and season with salt and pepper.
Preheat the broiler. In a large nonstick skillet, melt 1 tablespoon of the butter in the oil. Spread the couscous mixture in the skillet. Dot with the remaining 1 tablespoon of butter and cook over moderately high heat until golden on the bottom, about 5 minutes. Broil the galette 8 inches from the heat for about 5 minutes, until golden and sizzling. Using oven mitts, invert a large plate over the skillet. Carefully flip the galette out onto the plate, cut into wedges and serve.