Separate egg whites and yolks into two clean mixing bowls, being careful not to allow any yolks into the whites. (Otherwise they won’t mix correctly.) Whip the yolks until light, then add sugar and salt and whip until thick and white. Whip the whites until they form soft peaks. Fold whites into yolk mixture. Add milk, half-and-half, whipping cream, rum, and bourbon and stir until combined. Serve at once or pour into a mason jar, seal, and refrigerate.