Preheat oven to 350°F. Combine flour and sugar in a bowl. Add eggs, vanilla, and baking soda and mix until blended well. Stir in Louisiana mandarins. Grease and lightly flour a 9×13-inch pan. Pour batter into pan and bake for half an hour or until a toothpick inserted in center of cake comes out clean.
Glaze: Put brown sugar, milk, and butter in a saucepan and bring to a boil. Boil for two minutes then pour over the hot cake. Serve warm with ice cream or whipped topping. Serves 12-24.