Preheat oven to 350°F. Grease or line an 8x8 pan with parchment paper.
In bowl of stand mixer with paddle attachment on, cream 1/2 cup butter, 1/2 cup brown sugar, and 1/4 cup granulated sugar until light and fluffy for several minutes. Scrape sides down and beat in 1 egg. Scrape sides again.
Ina small bowl, combine 1 cup all-purpose flour, 1/2 teaspoon baking soda, a pinch of salt, 1 teaspoon ground cinnamon and 1/2 teaspoon ground nutmeg. Gradually add to creamed mixture and mix just until combined.
Toss 2 cups peeled and finely chopped apples in zest from one lemon and 1 tablespoon fresh lemon juice. Toast 1/2 cup chopped raw walnuts in small pan on stove over low heat, occasionally tossing walnuts to evenly heat. Add apples with lemon and walnuts to the cake batter and set the mixer on low just to get them going and then flash it on high for only a couple seconds to evenly mix them in.
Pour batter into prepared baking dish. Batter will be very thick so you will need to use a rubber spatula to spread it to an even layer. Bake in preheated oven for 30-35 minutes or until a toothpick inserted near the center comes out clean. Remove the cake from the pan.
Cake can be served warm or at room temperature. To serve, drizzle with caramel sauce (either store bought or homemade caramel sauce) and top with a pinch of flaked sea salt.
Notes
Make your own salted caramel sauce! Recipe here: https://selfproclaimedfoodie.com/salted-caramel-sauce/