Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Mix in the vanilla extract.
Add half of the dry ingredient mixture to the wet ingredients and mix until just combined.
Stir in the sour cream.
Add the remaining dry ingredients and mix until just combined, being careful not to overmix.
Toss the diced green apples with lemon juice to prevent browning.
Fold the diced green apples and chopped walnuts (if using) gently into the batter.
Pour the batter into the prepared cake pan and spread evenly.
Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.