Preheat oven to 350°F. Line muffin pans with liners and spray very well with nonstick cooking spray.
Stir eggs, applesauce, sugar, 1 teaspoon vanilla, cinnamon, salt, and baking powder in a large bowl until mixed. Stir in oats and milk.
Fill muffin cups 3/4 full. Bake for about 20-25 minutes until they get golden brown and no longer look wet in the center.
Make the glaze: whisk powdered sugar, 1/4 teaspoon vanilla, and milk. Drizzle over oatmeal. Serve warm.
Store in an airtight container for up to 3 days or freeze for up to 1 month. Microwave to reheat for fast morning breakfasts on the go.