Preheat the oven to 325 degrees F (160 degrees C). Grease a loaf pan.
Whisk All-Purpose Flour (1 1/2 cup), Ground Cinnamon (1 teaspoon), Ground Nutmeg (1/4 teaspoon), Salt (1/4 teaspoon) and Baking Soda (1/2 teaspoon) in a medium bowl until combined.
In the bowl of a stand mixer fitted with a whisk attachment, whisk the Canola Oil (1/2 cup), Granulated Sugar (1/2 cup), and Brown Sugar (1/4 cup) on medium-low speed until combined.
Add the Egg (2), one at a time, whisking well after each addition. Whisk in the Vanilla Extract (1 teaspoon).
Slowly add flour mixture to oil mixture on low speed until blended. Fold in Apple (2 cup) and Roasted Walnuts (1/2 cup) with a rubber spatula.
Pour batter into prepared loaf pan and bake for about 50 minutes.
While the cake is bubbling and browning in the oven, make the butterscotch icing. Combine Brown Sugar (1/4 cup) with Milk (2 1/2 tablespoon), Unsalted Butter (2 tablespoon), and Salt (1 pinch) in a small saucepan.
Heat over the icing over medium-low heat, stirring until sugar and salt have dissolved. Transfer to a bowl and let cool completely. Whisk in Powdered Confectioners Sugar (1/2 cup) until icing is smooth.
Let the cake cool on a wire rack. Drizzle the cooled cake with butterscotch icing, then slice and serve.