Preheat the oven to 350˚F. Butter a 9" X 5" loaf pan.
Bring the milk, butter, and salt to a simmer in a medium saucepan over medium heat. As soon as the liquid comes to a simmer, whisk in the corn flour. As it thickens, remove it from the heat. This should take about two minutes. Continue whisking and add the pumpkin purée and apple sauce. Cool slightly.
In a large bowl, whisk together the egg yolks, chives, and spices together.
Using an electric mixer, whip the egg whites until soft peaks form.
Whisk the corn flour into the egg yolks. Fold in the egg whites in thirds.
Scrape the batter into the loaf pan. Bake until the spoon bread is set and begins to pull away from the sides of the pan, about 40 minutes.
Let cool slightly before serving. It will continue to set up as it cools.