Preheat the oven to 350°F. Grease two 8” round cake pans; line with parchment, and grease the parchment.
Brown your butter. Place the pieces of butter in your light-colored pan. Turn the stove heat to medium. As your butter melts, begin stirring it with a spoon or rubber spatula consistently. Once melted, the butter will begin to foam and sizzle around the edges. Keep stirring. In about 5–8 minutes the butter will turn golden brown. It will smell intensely buttery, nutty, and rich. Be careful not to burn, as burnt butter will not taste good.
In a large bowl, whisk together the sugar, flour, salt, baking powder, baking soda, and pumpkin pie spice.In a separate medium-sized bowl, whisk together the eggs, buttermilk, pumpkin, browned butter, vanilla, and water. Add the wet ingredients to the dry ingredients, stirring to combine. Pour the batter into the prepared cake pans.
Bake the cakes for about 35 to 38 minutes, until a toothpick inserted into the center of one comes out clean.Remove the cakes from the oven and let them cool in the pans for 10 minutes. Turn them out onto a rack to cool completely.
BUTTERCREAM:
Add the butter and one cup of the powdered sugar to the bowl of a standing mixer fitted with the whisk attachment. Beat on low just to blend, then beat on high for 3 minutes, stopping to scrape down the sides of the bowl a few times.
Add your brown sugar and vanilla, heavy cream and another cup of powdered sugar. Beat on low speed to blend, then on high speed for another two minutes, stopping to scrape down the sides of the bowl a few times.
Add reamining powdered sugar and the salt. Beat on low to combine, then on high for about 1 minute, until the buttercream is completely smooth.
Check the consistency and beat in more powdered sugar if the buttercream is too thin. Taste, and add more salt if it's too sweet, or vanilla if desired.
ASSEMBLY:
Place one layer of cake on a cake stand or serving plate.
Top with approximately ? cup of buttercream and spread evenly.
Repeat with remaining layers.
Frost and smooth the outside with a thin crumb coat. Chill for 20mins.
After chilling, frost the remaining buttercream and smooth until you have clean, smooth lines.