Toss the diced apples with the cinnamon and brown sugar; set aside.
In a large mixing bowl whisk together the flour, salt, baking powder, baking soda and granulated sugar. Make a well in the center.
In a small mixing bowl lightly whisk the egg until blended. Add the sour cream, apple cider, butter and vanilla. Fold together with a spatula until smooth. Pour the sour cream mixture into the flour mixture. Gently fold together until the dry ingredients are just moistened. It will seem thick and a little dry, but keep folding.
Add the apple mixture and any accumulated juice to the batter. Gently fold with a spatula until the apples are incorporated.
Using an ice cream scoop (heaping), divide the batter between 8 or 9 muffin wells. Sprinkle the tops of the muffins generously with coarse sugar and chopped walnuts. Allow the muffins to rest for 10 to 15 minutes before baking.
Bake at 400 degrees F for 15 to 20 minutes or until a toothpick inserted in the center comes out with no wet batter.
Cool the muffins in the pan for 10 minutes, then remove to a wire rack to cool completely. Serve slightly warm if desired.