Heat the brown sugar in a medium skillet over medium-high heat and stir constantly using a rubber spatula until clumps are formed.
Add butter and continue to stir until everything has melted and become a dark 'amber-like' color. Continue to stir consistently until fully melted and bubbly, about 2-3 minutes.
Now, slowly whisk in the heavy cream and continue stirring until well incorporated and sauce has fully thickened.
Remove from heat, stir in the salt and allow to cool slightly before using. Set aside to cool completely before adding it to the recipe.
Begin by preheating your oven to 350 degrees Fahrenheit. Lightly grease (with butter) AND line with parchment paper the bottoms of THREE standard 8-inch cake pans.
In a bowl, whisk together the milk and apple cider vinegar or lemon juice and set aside for 5-10 minutes until everything "activates" to create the dairy-free "buttermilk". See Notes for Regular Buttermilk option.
In a large bowl, whisk together the flour, baking powder, cinnamon, and salt until combined.
In a bowl, add the butter and sugar, beating them together using a hand-mixer (on high-speed), until pale and fluffy, about 2-3 minutes.
Add the eggs (one at a time) followed by the egg yolks, vanilla, oil, yogurt, and salted caramel sauce, mixing until combined. On low-speed, add in the dry ingredients followed by the buttermilk and continue to mix until combined and the batter is smooth, about 3-4 minutes. NOTE: The batter should be thick, yet slowly run off the whisk once lifted.
Divide the batter evenly into each of the cake pans and bake for 30-35 minutes, or until a toothpick or butter knife comes out clean when tested in the centers.
Remove cakes from the oven and let them rest in the pan for 10 minutes or so before removing the cakes and placing them onto a cooling rack to fully cool. NOTE: Let them cool for at least 1-2 hours in a cool place.
Simply beat the butter in the bowl of an electric mixer (or using a hand-mixer) on medium-high speed, until smooth and pale. Add in the powdered sugar, vanilla, caramel sauce, and milk, continuing to mix on medium-speed until you reach the desired consistency----smooth and fluffy. NOTE: Add more milk (1 Tbsp at a time if too thick) or powdered sugar (for more thickness).
Place the first cake layer on your cake stand and evenly cover the top with buttercream. Now, top with 2nd layer and add more buttercream atop that layer. Finally, top with final layer and top with remaining buttercream, spreading it over the tops and sides of cake, evenly and fairly thinly.
Once fully frosted, add drizzles of salted caramel sauce to the top and sides, if desired. Chill for 5 minutes to ensure that buttercream sets.
When ready to serve, remove from the refrigerator. Slice and enjoy!
Bon Appetit!
