Preheat the oven to 350° F. Grease a 9x13-inch baking pan and line it with a piece of parchment paper.
In a large bowl, cream the ½ cup unsalted butter then add the 1 ¼ cups brown sugar and beat on medium speed for 2 minutes. Add the 1 cup applesauce then beat in the 2 eggs. The batter may look curdled - this is fine!
In a medium bowl, whisk together the 2 ½ cups gluten free flour, 1 ½ teaspoons baking soda, 2 teaspoons ground cinnamon, ½ teaspoon ground ginger, ½ teaspoon ground nutmeg, and ½ teaspoon fine sea salt
Beat the dry ingredients into the wet ingredients on low speed, then fold in the 1 cup chopped walnuts. Pour the batter into the prepared pan and let rest for 15 -20 minutes.
Place the cake in the oven and bake for about 35 minutes, until a toothpick inserted in the middle comes out clean. Remove from oven and place on a rack to cool for 30 minutes, then dust with powdered sugar if using. Cut the cake into pieces directly from the pan and serve.
Notes
CN's tips
Don't worry if the batter "breaks." After creaming the butter and sugar, when adding the applesauce and eggs, the mixture has a tendency to look curdled. This is perfectly fine; when the batter is fully combined, it will smooth out.
Try some almond flour. For extra richness and moisture, substitute ½ cup of the gluten-free flour for fine-ground almond flour.
Make it dairy-free. Swap non-dairy butter or a neutral oil for the butter.
Try a spice blend. Simplify life and use a spice blend such as an apple pie spice blend or pumpkin pie spice in place of the combination of spices.
Make a pumpkin cake. Switch out the applesauce for pumpkin! Use 1 cup of pure pumpkin puree instead of the applesauce. Or just make my gluten free pumpkin sheet cake recipe.
Bake it as a layer cake. You can make this into a more elaborate cake by baking the batter in two 8 or 9-inch cake rounds, then filling and frosting them with a cream cheese frosting or a simple vanilla buttercream.