In a small saucepan over medium heat, melt 1 cup of the butter.
Cook the butter, stirring it gently and constantly, until it becomes amber-brown and starts to smell nutty, about 2-3 minutes.
Transfer the butter to the refrigerator until it solidifies again, about 1-2 hours.
Preheat the oven to 325 degrees F.
Liberally coat a fluted tube pan with nonstick spray.
In a mixing bowl, add the browned butter and the shortening and beat with an electric mixer on high speed for 2 minutes.
Slowly add in 2 cups of the granulated sugar and beat on high speed until the mixture becomes very pale yellow and fluffy, about 7 minutes.
Add the eggs, 1 at a time, and combine well after each addition. Scrape down the sides of the bowl as needed.
With the mixer at the lowest speed, slowly add the flour into the batter in two separate increments.
Add the salt, the baking powder, and the baking soda to the batter mixture and mix until just combined, being careful not to overmix.
Add the buttermilk and 1 tablespoon of the vanilla to the batter mixture and mix, scraping down the sides of the bowl periodically, until just combined.
Add the batter to the prepared tube pan.
Bake until a toothpick inserted into the center comes out mostly clean but still moist, about 45-55 minutes.
Allow the cake to cool for 10 minutes.
Invert the cake onto a serving plate.
In a saucepan over medium heat, melt the remaining butter and cook until browned, about 3-4 minutes.
Turn off the stovetop heat.
Add in the remaining granulated sugar, the water, and the remaining vanilla and whisk until smooth.
Poke the still warm cake with a toothpick or a skewer in several places all over the surface.
Pour the brown butter glaze over the cake, allowing it to seep into the holes.
Serve dusted with the powdered sugar.