In a small bowl, combine the brown sugar, flour and cinnamon.
Drizzle over the melted butter and, using a fork (or use your fingers), mix the ingredients are well blended and form small crumbs.
Add chopped walnuts and mix into topping.
Pop in the frig while you make the cake batter.
Position an oven rack in the center of the oven. Heat oven to 350°F. Lightly grease and flour the sides and bottom of a 9" round springform pan. Wrap the bottom and up 1" of the pan tightly with aluminum foil to prevent dough from leaking while baking.
In a medium bowl, combine the flour, baking soda, cinnamon, nutmeg and salt. Whisk until well blended.
In a large bowl, beat butter, sugar and vanilla with an electric mixer fitted with the paddle attachment on medium speed until well blended, about 3 minutes.
Add the eggs, one at a time, beating well after each addition. Stop to scrape the bowl and beaters as needed.
Add about half of the flour mixture and mix on low speed just until blended. Add the yogurt and continue mixing just until blended. Using a rubber spatula, fold in the remaining flour mixture.
Scrape half of the batter (about 1lb 2 ounces for those of you who use a scale) into the prepared pan and spread evenly.
Evenly scatter half of the streusel mixture over the batter.
Spoon the remaining batter evenly over the streusel and spread evenly.
Arrange slices from two of the apples around the top of the cake, pushing in slightly.
Scatter the remaining streusel evenly over the top.
Bake until the top is browned and a pick inserted in the center of the cake comes out clean, approximately 45-50 minutes. Cool the pan on a wire rack until warm or room temperature.
Cut remaining apple slices in half and saute in teaspoon of butter for two minutes. Drizzle with some caramel sauce, mix thoroughly and mound in center of coffee cake.
Drizzle entire cake with more caramel sauce.
