Bring 1 quart water to a simmer in a 3-quart pan with a tight-fitting lid. Melt the butter in a 10-inch skillet or saute pan over medium-high heat. When sizzling, add the scallions. Cook, stirring frequently, for about 1 minute, then add the rice, turn to coat it with the butter, and cook for a minute or two. Stir in 1/2 teaspoon salt. Add the rice to the simmering water. Cover and cook over low heat for 16 minutes. Remove the lid, and if there’s still water present, cook it off. Otherwise, stir in the lemon zest, parsley, pepper, and cheeses, then allow the rice to cool in the pan. Stir in one of the eggs.