Combine the eggs, dark corn syrup, dark brown sugar, 1 tsp vanilla extract, cubed unsalted butter, and 0.5 tsp salt in a saucepan. Heat over medium heat, stirring constantly, until the mixture begins to boil.

Add the chopped pecans to the boiling mixture and continue to boil for 30 seconds, stirring constantly.

Remove the pecan filling from the heat and transfer it to a heatproof bowl. Refrigerate until completely cool and thickened, at least 2-3 hours or overnight.

Preheat your oven to 350°F (176°C). Prepare three 8-inch round cake pans by greasing the sides and lining the bottoms with parchment paper circles.

In a large mixing bowl, cream the room temperature unsalted butter, packed light brown sugar, and granulated sugar together until the mixture is light in color and fluffy, about 3-4 minutes. Do not skimp on creaming time.

Add the room temperature sour cream and 2 tsp vanilla extract to the creamed mixture and mix until just well combined.

Add the large egg whites in two batches, mixing thoroughly after each addition until well combined. Scrape down the sides of the bowl as needed to ensure all ingredients are incorporated.

In a separate medium bowl, whisk together the all-purpose flour, baking powder, ground cinnamon, and 0.5 tsp salt. In a small measuring cup, combine the milk and water.

Add half of the dry ingredients to the wet batter and mix on low speed until just combined. Then, add the milk and water mixture and mix until combined. Finally, add the remaining dry ingredients and mix until just combined. Scrape down the sides of the bowl as needed.

Divide the cake batter evenly among the three prepared cake pans. Bake for approximately 21-23 minutes, or until a toothpick inserted into the center of a cake comes out with a few moist crumbs.

Remove cakes from the oven and allow them to cool in their pans for about 2-3 minutes. Then, invert them onto wire cooling racks to cool completely before assembling.

To make the frosting, combine the room temperature salted butter and vegetable shortening in a large mixer bowl. Beat on medium-high speed until smooth and creamy.

Add about half of the powdered sugar to the butter mixture and mix on low speed until well combined.

Stir in the 1 tbsp vanilla extract, 1 tsp ground cinnamon, and 3-4 tablespoons of water or milk. Mix until smooth.

Add the remaining powdered sugar and mix until thoroughly combined. Add additional water or milk, one tablespoon at a time (up to 6 tbsp total), as needed to reach your desired smooth, spreadable consistency.

To assemble the cake, use a large serrated knife to carefully level the tops of the cooled cake layers, removing any domes to create flat surfaces.

Place the first leveled cake layer on a serving plate or cardboard cake round. Pipe a dam of frosting around the outer edge of this layer to hold the filling.

Spread about one-third of the cooled pecan pie filling evenly inside the frosting dam on the first cake layer.

Carefully place the second cake layer on top and repeat the process: pipe a frosting dam, then spread another one-third of the pecan pie filling inside.

Add the final cake layer on top. Apply a thin layer of frosting (crumb coat) to the entire cake, smoothing it over the top and sides. Refrigerate for 15-20 minutes to set the crumb coat.

Apply the remaining frosting to the outside of the cake, striving for a smooth finish. Use an offset spatula or bench scraper for best results.

Finish the cake by piping a decorative border around the top edge. Fill the center of this border with the remaining pecan pie filling. Gently press pecan halves into the sides of the cake for decoration.

Refrigerate the assembled cake until ready to serve. For best flavor and texture, allow the cake to come to room temperature for about 30-60 minutes before slicing and serving. The cake is best enjoyed within 2-3 days when stored in an airtight container in the refrigerator.