Preheat oven to 400°.
Line 2 12-hole muffin pans with paper liners; set aside.
In a large bowl, cream together applesauce, olive oil, Egg Beaters and sugar.
Reserve 3 tablespoons flour. In a medium bowl, combine remaining flour,
baking powder, salt and baking soda.
Combine milk and vanilla.
Alternately add milk and flour mixtures to creamed oil and egg mixture. Place cranberries in a large bowl, sprinkle with reserved flour and turn gently with a large spoon until cranberries are lightly coated. Fold cranberries into batter.
Fill each muffin well ¾ full and sprinkle tops with sugar. Fill any remaining empty wells ½ full with water. Bake until muffins pull away from sides of pan and turn golden brown and crumb on sides or until tester comes out clean, about 15 to 20 minutes.
Per serving: 3 g total fat
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