In a small saucepan, combine the apples, sugar, water and brown sugar. Bring to a boil over medium heat. Sprinkle with flour; cook and stir for 2 minutes or until thickened. Stir in butter and lemon juice. Remove from the heat; add vanilla. Set aside to cool.
For topping, combine the brown sugar, flour and oats. Cut in butter until mixture resembles coarse crumbs; set aside.
In a large bowl, combine the flour, sugar, baking powder, cinnamon and salt. In another bowl, beat the egg, milk and oil. Stir into dry ingredients just until moistened. Fill greased or paper-lined muffin cups three-fourths full. Drop apple mixture by tablespoonfuls into the center of each muffin. Sprinkle with topping.
Bake at 400° for 20-24 minutes or until a toothpick inserted in muffin comes out clean. Cool for 5 minutes before removing from pan to a wire rack. Combine glaze ingredients; drizzle over muffins. Serve warm.