Preheat your oven to 350°F (180°C). Line the bottoms of three 8-inch round cake pans with parchment paper to prevent sticking. Lightly butter and flour the sides of each pan to ensure the cakes release easily after baking.
In the bowl of a stand mixer fitted with the paddle attachment, combine the pumpkin puree, packed light brown sugar, vegetable oil, and eggs. Beat at medium speed until the mixture is smooth and well blended, about 1 minute. Separately, in a medium bowl, whisk together the all-purpose flour, 1 1/2 tablespoons pumpkin pie spice, baking powder, baking soda, and 1 teaspoon kosher salt. With the mixer on low speed, slowly add the dry ingredients to the wet mixture. Beat just until combined, then gently fold in the chopped walnuts.
Divide the prepared batter evenly among the three prepared cake pans. Smooth out the tops with a spatula. Bake in the preheated oven for 28 to 30 minutes, or until a wooden pick inserted in the center comes out clean. Let the cakes cool in their pans for 10 minutes, then carefully remove them from the pans and transfer to wire racks to cool completely before frosting. I always let cakes cool fully so the frosting doesn't melt and slide off—patience pays off here!
While the cakes cool, make the frosting. In the bowl of a stand mixer with the paddle attachment, beat the room temperature butter at medium speed until it's smooth and creamy, about 2 minutes. Gradually add the powdered sugar, 1 cup at a time, beating well after each addition and scraping down the sides of the bowl when needed. Beat in the heavy cream. Add the remaining pumpkin pie spice and salt, and continue to beat until the frosting is fluffy and smooth. For an extra touch, I like to add a pinch of extra pumpkin spice if you want it really aromatic.
Place one cooled cake layer on your serving plate. Spread about 1 cup of the prepared Pumpkin Spice Frosting evenly over the first layer. Place the second cake layer on top and repeat with another cup of frosting. Place the third cake layer on and cover the top and sides with a light layer of frosting. Refrigerate the cake for about 30 minutes to set the frosting, making it easier to decorate. Chilling keeps things tidy when you pipe decorative frosting on later.
Once the cake is chilled, divide the remaining frosting into two portions. Place half in a pastry bag fitted with a 4B star tip, and the other half in a bag with a Wilton 2A round tip. Pipe the frosting decoratively on the top of the cake as you like. Serve the cake immediately or cover and refrigerate for up to 3 days.