In a small bowl, combine the brown sugar, flour, cinnamon, and chopped nuts (if using). Cut in the softened butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Set aside while you prepare the cake batter.
In a large bowl, whisk together the all-purpose flour, granulated sugar, baking powder, baking soda, salt, and cinnamon until well combined.
Using a hand mixer or stand mixer, beat the softened butter until creamy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Alternately add the dry ingredients and buttermilk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined, being careful not to overmix.
Gently fold the peeled and chopped apples into the batter, ensuring they are evenly distributed.
Pour the batter into the greased 9x13-inch pan, smoothing the top with a spatula. Sprinkle the crumb topping evenly over the batter. Bake in a preheated 350°F (175°C) oven for 45-50 minutes or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for at least 15 minutes before slicing. Serve warm or at room temperature, perfect on its own or with a dollop of whipped cream.