In a bowl, combine the thinly sliced apples, lemon juice, granulated sugar, ground cinnamon, and a pinch of salt. Toss until the apples are evenly coated.

Place the apple mixture in a medium to large pot over medium-high heat. Slowly bring it to a boil, stirring occasionally.

In a separate small bowl, create a slurry by mixing 2 tablespoons cornstarch with ¼ cup cold water. Set it aside.

As the apples release liquid and begin to soften, add the slurry to the mixture while stirring constantly. The mixture should thicken within about 30 seconds to a consistency where it can hold together when lifted with a spoon. If needed, prepare a bit more slurry to reach the desired thickness.

Once thickened, remove the apple mixture from heat and transfer it to a container. Let it cool down to room temperature. The filling can be stored in an airtight container in the fridge for up to 1 week.

Preheat your oven to 325°F. Spray two 6-inch round cake pans with non-stick cooking spray, line with parchment paper, and spray again. Set aside.

In a medium-sized mixing bowl, whisk together the flour, cinnamon, nutmeg, salt, and baking powder. Set this dry mixture aside.

In a large bowl, combine the granulated sugar, brown sugar, and vegetable oil. Whisk by hand for about 1 minute until well combined.

Add the dry ingredients to the wet ingredients and gently fold the mixture together until evenly combined and there are no flour streaks. Be careful not to overmix.

Evenly distribute the batter into the prepared cake pans. Use the back of a spoon to smooth out the batter for even baking.

Bake in the oven for 30-35 minutes, or until a toothpick inserted into the center of the cakes comes out clean. While the cakes are cooling, make the brown butter frosting.

In a medium-sized saucepan, melt the butter over medium heat. Continue to cook, stirring constantly, until the butter foams, the milk solids separate, and the butter begins to brown and emit a nutty aroma. Watch closely to prevent burning. Once browned, remove from heat, transfer to a glass bowl, and let it cool completely to room temperature.

In the bowl of a stand mixer fitted with the paddle attachment, combine the browned butter and room temperature cream cheese. Beat on medium-high speed for 2-3 minutes until creamy, scraping down the sides of the bowl as needed.

Gradually add the powdered sugar, starting with 5 cups, then add the vanilla extract, heavy cream, and a pinch of salt. Mix on low speed until just combined, then increase to medium speed and beat for an additional 2 minutes. If the frosting is too thick, add more cream or powdered sugar to achieve the desired consistency.

Place a small dollop of frosting in the center of your cake board to act as glue. Place the first cake layer, top side up, on the cake board. Spread about ½ cup of frosting evenly over the top. With a piping bag or a ziplock bag, pipe a rim around the edge of the cake.

Apply the cooled apple filling and, with the back of a spoon, evenly spread it across the top of the cake. Get eye level with it to ensure it's even.

Place the second cake layer, top side down, on top of the frosting. Apply a thin crumb coat of frosting over the entire cake to lock in any crumbs. Freeze the cake for 10-15 minutes to set the crumb coat.

Frost the cake with the remaining brown butter frosting, ensuring smooth, even coverage. Use a cake comb to achieve the sides or frost it however you like. Top with extra apple filling if desired. Serve the cake at room temperature.