Prepare the doughnuts: Preheat the oven to 325 degrees F. Lightly spray a doughnut pan with nonstick cooking spray. In a large bowl, mix flour, cake mix, sugar, baking powder, and salt. Stir in milk, eggs, vanilla and melted butter. Mix until well combined. Stir in the sprinkles. Scrape the batter into a large zip bag, snip the corner and squeeze the batter into the doughnut shapes in the pan- only filling 1/2 to 3/4-full. Bake 8 to 10 minutes, until the doughnuts spring back when touched. Cool the doughnuts completely before adding the icing.