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 bowl, whisk together the flour, baking powder, pumpkin pie spice, cardamom, cinnamon, ginger, nutmeg, and salt until combined. Set aside.
1 ½ cups all-purpose flour, 1 tablespoon baking powder, ½ teaspoon pumpkin pie spice, ¼ teaspoon ground cardamom, 1 ½ teaspoons ground cinnamon, ½ teaspoon ground ginger, ¼ teaspoon ground nutmeg, ¾ teaspoon salt
In the bowl of an electric stand mixer fitted with the paddle attachment, cream the granulated sugar, brown sugar, and eggs on medium speed until light and fluffy, about 5 minutes.
⅔ cup granulated sugar, ½ cup light brown sugar, 3 large eggs
Add the vegetable oil and vanilla extract, and beat on medium speed until fully incorporated, about 30 seconds. Add the pumpkin purée and mix on low speed until combined, about 30 seconds more.
½ cup vegetable oil, 1 teaspoon pure vanilla extract, 1 cup pumpkin purée
With the mixer on the lowest speed, gradually add the dry ingredients to the pumpkin mixture, mixing until just combined.
Evenly distribute the batter between the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean or with just a few crumbs.
Let the cakes cool in the pans for 20 minutes, then transfer them to a wire rack to cool completely. Once they reach room temperature, wrap them in plastic wrap and store them in the fridge for up to 5 days, or in the freezer for up to 6 months.
For 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. Once browned, remove from heat, transfer to a glass bowl, and let it cool completely to room temperature.
½ cup unsalted butter
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.
4 ounces cream cheese
Gradually add the powdered sugar, starting with 5 cups, then 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.
5-6 cups powdered sugar, 1-2 tablespoons heavy whipping cream, 1 teaspoon vanilla extract, Pinch of salt
Assembly
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 1 cup of frosting evenly over the top.
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. Serve the cake at room temperature.