Combine flour, sugar, and cinnamon in a small bowl; cut in butter until mixture resembles a coarse meal.
Stir in nuts and set mixture aside.
Preheat oven to 375°F.
Lightly butter a 12-cup muffin pan or line with muffin cups.
Whisk together flour, baking powder, baking soda, salt, and set aside.
Cream butter, sugar and cinnamon until light and fluffy.
Add eggs beating well after each addition. (If mixture begins to curdle, blend in a tablespoon of the flour mixture.) Stir in milk and applesauce.
Fold in flour mixture until dry ingredients are combined and moistened. (Use low speed on the mixer or fold in by hand.) Do not over mix.
Spoon batter into prepared muffin cups.
Sprinkle topping evenly over batter.
Bake 20 to 25 minutes or until lightly browned.