Make the salted caramel by adding 140 g sugar and 1 1/2 tbsp water to a medium heavy saucepan and cook over medium heat, swirling occasionally, until the sugar melts and turns a deep amber color.
Remove the pan from the heat and carefully whisk in 150 g heavy cream, then 40 g butter, whisking until smooth.
Stir in 1/2 tsp fine sea salt, then pour the caramel into a shallow bowl and refrigerate until thickened and at room temperature, about 30 to 60 minutes.
Preheat the oven to 340°F and line three 8 inch round cake pans (20 cm) with parchment paper on the bottoms and lightly grease the sides.
In a medium bowl sift together the flour, cornstarch, baking powder, baking soda, and salt, then set aside.
In a large mixing bowl beat 180 g butter and 300 g sugar on high speed for 3 minutes until light and fluffy, scraping the bowl once.
Add the eggs one at a time, beating on medium after each addition until fully combined.
On low speed mix in half of the dry ingredients just until combined.
Add the sour cream, vegetable oil, and vanilla bean paste and mix on low until just combined.
Add the remaining dry ingredients and mix on low until the batter is smooth with no dry streaks.
Use a rubber spatula to gently fold the batter once or twice to make sure everything is evenly combined.
Divide the batter evenly among the three prepared pans and smooth the tops.
Bake for 19 to 22 minutes, or until the centers spring back lightly to the touch and a tester inserted in the center comes out clean.
Cool the cakes on a rack for 10 minutes, then run a knife around the edges, turn them out onto the rack, and let them cool completely.
For the buttercream, sift the powdered sugar into a large bowl and set aside.
In a stand mixer fitted with the paddle, beat 400 g butter on medium high speed for 4 minutes, scraping down the sides once, then beat 2 minutes more until very light and creamy.
On low speed add half of the powdered sugar, then the vanilla bean paste and 3 tbsp cooled salted caramel, mixing until fully incorporated.
Add the remaining powdered sugar and mix on low until combined, then beat 1 minute on low to smooth the buttercream.
If needed, level the cooled cake layers with a serrated knife so the tops are flat.
Place the first cake layer on a serving plate and spread a thin layer of buttercream over the top.
Pipe or spread a buttercream border around the edge of the layer, then spoon some cooled caramel inside the border and spread it gently.
Top with the second cake layer and repeat the buttercream and caramel filling.
Place the third cake layer on top and spread a thin crumb coat of buttercream over the top and sides of the cake.
Chill the crumb coated cake in the refrigerator for 20 minutes to set the frosting.
Add the remaining buttercream over the top and sides of the chilled cake and smooth or swirl as desired.
Drizzle additional cooled salted caramel over the top, letting some drip down the sides, and garnish with flaky sea salt just before serving.