In a large saucepan, combine the honey, salt, butter and 3 cups of the milk. Bring to a boil over medium heat.
Meanwhile, in a small bowl, whisk together the cornmeal and remaining 1 cup of milk. Add the cornmeal mixture gradually to the milk mixture, whisking until smooth. Reduce the heat to low, cover, and cook, whisking occasionally, for 5 minutes.
In a small bowl, beat the eggs. Stir 1 cup of the hot cornmeal into eggs and whisk until smooth. Gradually stir the cornmeal-egg mixture back into the saucepan. Cover, and cook on low heat until thick, stirring frequently. Ladle into serving bowls and serve immediately with milk, if desired (I like mine without the milk)