1 stick unsalted butter, melted and cooled, plus more softened butter for oven dish
1 cup flour
1 tsp cinnamon
½ tsp baking powder
½ tsp salt
¼ tsp baking soda
1 cup sugar
1 large egg, beaten
½ tsp vanilla
½ cup chopped walnuts
2 large apples, peeled, cored and cut into small cubes (about 2¾ cups)