Preheat oven to 350°F. Line a 9x5" bread pan with parchment paper and set aside.
Chop the Granny Smith apples into about 1/4-inch pieces and place them in a medium bowl. Add 1 tablespoon lemon juice and 2 teaspoons cinnamon, stir to coat, and set the apples aside while you make the batter.
In a large bowl, cream 1/2 cup softened salted butter and 3/4 cup white granulated sugar until light and fluffy, about 3–4 minutes.
Add the 3 large eggs, 2 teaspoons vanilla extract, and 1/2 teaspoon salt to the butter mixture and beat until well combined and creamy, about 2–3 minutes, scraping down the sides of the bowl as needed.
In a separate bowl, whisk together 2 cups all-purpose flour, 1 teaspoon baking powder, and 1/2 teaspoon baking soda.
Add the flour mixture to the butter mixture alternately with 1/2 cup buttermilk, beginning and ending with the flour mixture, and mix only until just combined.
Stir in half of the prepared apple mixture. If using, fold in 3/4 cup chopped walnuts.
Pour the batter into the prepared 9x5" pan and smooth the top. Spread the remaining apples evenly over the batter.
In a small bowl, combine 1/4 cup brown sugar and 1 teaspoon cinnamon; sprinkle this mixture evenly over the apples on top of the batter.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean. If the top is browning too quickly, tent loosely with foil.
Remove the bread from the oven and let it cool in the pan for at least 15 minutes.
While the bread cools, make the glaze by stirring together 1/2 cup powdered sugar and 1 tablespoon whole milk or cream until smooth.
Drizzle the glaze over the warm (but not piping hot) bread, then slice and serve.