Preheat oven to 350 degrees F. In a medium baking dish, combine cranberries and brown sugar. Mix well. Spread cranberry mixture over bottom of dish.
In a medium bowl, combine milk, cornmeal, and salt. In a large saucepan, bring water to a boil over high heat. Reduce heat to low; whisk cornmeal mixture into water. Cook , whisking constantly, until cornmeal mixture thickens and bubbles, about 5 minutes. Remove from heat.
In a small bowl, beat eggs with 1/4 cup of cornmeal mixture. Whisk egg and cornmeal mixture back into saucepan.
In a medium mixing bowl, using an electric mixer set on high speed, beat egg whites until stiff peaks form. Fold egg whites into cornmeal mixture. Spread cornmeal mixture over cranberry mixture in prepared dish.
Bake spoon bread until golden and a knife inserted into center comes out clean, about 40 minutes. Serve immediately.