Peel and core apples and slice them into thin wedges. (First, I cut an apple into quarters, and then each quarter into 3 slices. Alternatively, you can cube the apples into small pieces.)
In a medium bowl, whisk together flour, baking powder, baking soda and salt.
In a mixing bowl with paddle attachment, beat butter and sugar until fluffy, about 2 minutes.
Add eggs one at a time, beating well after each addition and scraping the sides of the bowl half way.
Add the flour mixture and mix on low speed until just combined.
Then add applesauce and vanilla extract and mix it for a minute.
Finally, add the remaining flour mixture and stir until combined.
Pour the cake batter into the prepared cake pan. Arrange the apple slices on top and spread the prepared streusel topping evenly all over. (If you chopped apples into cubes, you can stir them into the batter instead.)
Bake the cake for 50-55 minutes, or until inserted toothpick comes out clean.
Cool the cake on wire rack for 5 minutes, then remove the sides of the pan and cool the cake completely. Serve the coffee cake with homemade caramel sauce, if desired. You can keep the cake at room temperature, covered, for up to 2 days. Or refrigerate it for up to 5 days. This cake also freezes well.