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1
Preheat oven to 400 F. Line two muffin pans with paper liners.
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2
Add the diced apples, butter, sugar, cinnamon and water to a skillet and set over medium heat. Cook, stirring occasionally, until the apples are tender, about 8-10 minutes. Let the apples cool slightly then toss them with the flour to coat.
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3
Whisk the flour, baking powder, baking soda, cinnamon and salt in a medium bowl. In a large bowl, whisk the applesauce, oil and both sugars until smooth and well combined. Add the eggs, one at a time, beating after each addition. Stir in the vanilla. Alternately add the dry ingredients with the buttermilk, starting and finishing with the dry ingredients, and stirring gently just until the ingredients are combined. Fold in the apples.
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4
Divide the batter among the prepared liners, filling each almost to the top. Bake for 14-16 minutes, or until the muffins are golden and spring back when gently pressed on the top. Transfer the pan to a wire rack and let the muffins cool in the pan for 5 minutes before removing them to the rack. Let cool slightly while you make the glaze.
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5
To make the glaze: Whisk the melted butter, confectioners' sugar, vanilla and water in a small bowl until smooth.
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6
When muffins have cooled slightly, hold the muffin upside down and dip the top into the glaze. Allow to set, then dip a second time and let harden again before serving.
