Preheat and prepare pan. Preheat oven to 375oF. Line pan with paper muffin cups or grease the wells and top of pan with non-stick cooking spray.
Make crumb topping. In a small bowl, combine flour, salt, brown sugar, granulated sugar and cinnamon. Work butter into mixture until crumbly. Set aside.
Combine dry ingredients. Whisk together the flour, brown sugar, baking powder, salt, and spices in a large bowl. Make a well in the center by pushing the dry ingredients to the side and creating a hole in the middle.
Combine wet ingredients. In a second mixing bowl, whisk together oil, milk, eggs, and vanilla extract.
Add wet to dry. Pour wet ingredients all at once into the well in the flour mixture. Mix quickly and lightly with a rubber spatula, but do not overbeat. The batter will be lumpy. Stir in apples. Divide the batter into the wells, filling each well.
Sprinkle on crumb topping.
Bake muffins. Bake for 25 minutes, or until golden and a toothpick inserted comes out clean. Allow to cool in the pan for 5 minutes, then transfer each muffin to a wire cooling rack to continue to cool.
Make icing. In a small mixing bowl, stir together all icing ingredients. Adjust consistency if needed. Drizzle on cooled muffins.