Pre heat oven to 350 degrees and line the long side of a 9 x 5 loaf pan with parchment paper. The parchment paper should make a sling and hang off the sides of the pan for easy removal.
In a small saucepan, melt butter over medium heat. Alternatively, place butter in a microwave safe bowl and microwave until melted.
In a small bowl, mix cinnamon and brown sugar until evenly combined. Set aside.
In a large bowl, whisk together flour, baking soda, baking powder, and salt. Set aside
In a medium size bowl, mix together sour cream and milk. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat eggs and granulated sugar on medium speed until pale yellow, about 2 - 3 minutes.
With the mixer on low, slowly add melted butter and mix until evenly combined. Stir in vanilla extract.
With the mixer on low, add flour mixture alternatively with the sour cream mixture, beginning and ending with the flour mixture. Flour mixture should be added in 3 additions and sour cream mixture in 2. Mix until just combined after each addition, being careful not to over mix. Add grated apples to the batter and gently fold with a rubber spatula until evenly incorporated.
Pour 2 cups of batter into prepared pan and firmly tap pan on counter to get rid of air bubbles. Sprinkle with half of cinnamon sugar mixture. Spoon remaining batter over top of cinnamon sugar mixture followed by the remaining cinnamon sugar mixture. Gently press toasted walnuts on top of batter.
Bake for 45 to 50 minutes until golden brown (mine was ready in 50 minutes) and cake tester inserted into the center comes out clean. Allow bread to cool in pan on wire rack for 10 minutes then using the parchment sling, lift bread out of pan and place onto wire rack. Let bread cool completely before slicing.