Heat half the butter and 2 tablespoons of oil in a heavy-based pan suitable for making risotto. Sauté the shallots over low heat until light gold and then stir in the rice with a wooden spoon. Stir for a few minutes to completely coat the rice and let it cook just a bit. Add the wine and when that has evaporated, add all of the broth. Add a few good grinds of nutmeg and taste for salt (your broth will probably be seasoned enough). Simmer uncovered over high heat for about 15 minutes, or until the rice has absorbed much of the liquid. If it seems as if it needs a bit more liquid, add some hot water. Remove from the heat and stir in the remaining butter and the parmesan. Taste for salt, adjusting if necessary. Leave with the lid on so that the steam continues to cook the rice.
Heat the remaining oil in a large non-stick frying pan and briefly fry the sage leaves until crisp. Remove with tongs. Gently break the eggs into the pan and sprinkle a little salt on the yolks. Cook until the edges of the white are a bit golden. Cover the pan with a lid and fry until the yolks are just slightly opaque on the surface but still soft inside (they are best when the undersides are golden and a bit crisp).
Scoop the rice onto serving plates and top each serving with an egg and a couple of sage leaves, being careful not to break the yolk just yet. Serve with a sprinkling of parmesan and a few grinds of black pepper for those who want it.