Preheat oven to 350°F. Prepare three 9-inch cake pans: grease each with shortening and dust with flour, tapping out the excess.
In a large bowl whisk together 3 cups (360 g) all-purpose flour, 2 teaspoons (8 g) baking powder, 1 teaspoon (6 g) baking soda (for the cake), and a pinch (0.4 g) kosher salt. Set aside.
In the bowl of a stand mixer fitted with the paddle (or in a large bowl with a hand mixer), cream 1 cup (226 g) softened butter with 2 cups (396 g) sugar until light and fluffy, about 8 minutes.
Add the 4 eggs, one at a time, mixing until each egg is fully incorporated before adding the next.
With the mixer on low, add the dry flour mixture and 1 cup (227 g) room-temperature buttermilk alternately, beginning and ending with the flour mixture (dry–wet–dry–wet–dry). Mix each addition just until combined, and after each time the flour is incorporated briefly raise the mixer to medium-high for 5–10 seconds to lighten the batter.
Add 2 teaspoons (9.4 g) vanilla extract and mix until incorporated. After the vanilla is incorporated, beat on high for about 10 seconds to further lighten the batter.
Divide the batter evenly among the three prepared pans, smooth the tops, and bake 25–30 minutes, or until the cakes are set and a toothpick inserted in the center comes out clean. Cool in the pans for about 10 minutes, then turn the cakes out onto cooling racks and allow to cool completely.
While the cakes cool, make the caramel stage of the frosting: in a 3–4 quart pot combine 2 cups (396 g) sugar, 1 cup (227 g) buttermilk, 1/2 cup (92 g) shortening, and 1/2 cup (113 g) butter. Stir with a wooden spoon over medium-low heat until melted and combined.
Once the mixture is combined and simmering, add 1 teaspoon (6 g) baking soda (the baking soda for the frosting). Stir carefully—the mixture will bubble. Continue cooking over medium-low, stirring as needed, until the mixture reaches the softball stage (235–245°F on a candy thermometer) or passes the cold water test.
Remove the pot from the heat and carefully pour the hot caramel into a large mixing bowl or the bowl of a stand mixer. Allow it to cool until it is warm but no longer hot to the touch (safe to touch lightly). Attach the whip attachment and begin whipping the cooled caramel.
With the mixer running on medium, add the remaining 1/2 cup (113 g) butter and 1/2 teaspoon (3.25 g) sea salt to the whipped caramel. Whip until the butter and salt are fully incorporated and the mixture is smooth.
Add 2 cups (227 g) confectioner’s sugar to the frosting in four 1/2-cup increments. After each 1/2-cup addition, stop to scrape down the sides of the bowl, then turn the mixer onto high for about 10 seconds to incorporate air. Continue until all 2 cups are added and the frosting holds shape.
If the frosting is still too loose after all the confectioner’s sugar is incorporated, chill the frosting briefly (10–30 minutes) and re-whip until it reaches a spreadable, pipeable consistency.
Assemble the cake: place one cooled layer on a cake plate, spread an even layer of frosting, add the second layer, repeat, then frost the top and sides of the cake. Store the finished cake on a cake plate covered with a dome or in an airtight container. Best served within 1–3 days.