Preheat oven to 350 degrees F (175 degrees C). Grease and flour a Bundt cake pan.
To make streusel: In a medium bowl, mix brown sugar, 3/4 cup flour, and cinnamon. Cut in the butter with a fork until crumbly. Stir in walnuts.
In a medium bowl, stir together 3 1/4 cups flour, baking powder, and baking soda. In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, mixing well after each. Then stir in the vanilla and yogurt. Gently stir in the flour mixture just until blended.
Pour 3 cups of the batter into the Bundt pan, sprinkle with 1/4 of the streusel, and layer with apples. Sprinkle with 1/2 the remaining streusel. Pour in the remaining batter, and top with the remaining 1/4 streusel. Lightly pat the top layer of streusel so it sticks to the cake batter.
Bake 50 to 60 minutes in the preheated oven, or until a toothpick inserted in the center comes out clean. Cool in the pan on a wire rack 15 minutes. Place cookie sheet over pan and carefully invert both. Remove Bundt pan, and let the cake cool completely.