Add the apple cider to a small saucepan and bring to a boil. Cook until reduced to 1/2 cup, about 15-20 minutes. Remove from the burner and let cool.
Next, make the caramel sauce. Melt the sugar in a small saucepan over medium heat, about 5-6 minutes, stirring constantly. When the granules are totally dissolved and turn a rich golden color, add the butter. Be VERY careful - it will probably splatter! Melt the butter while stirring constantly. Carefully pour in the heavy cream, stirring, and simmer 2-3 minutes until thickened. Remove from the heat and add the salt and vanilla. Let cool - the caramel will continue to thicken. Unused caramel will keep for up to a week in the fridge.
Preheat oven to 350 degrees. Grease 2 9 inch cake pans with butter or oil.
In a large bowl, beat the butter, sugar, and brown sugar until fluffy, about 3-4 minutes. Beat in the eggs, one at a time, until fully incorporated. Whip in the vanilla and Greek yogurt. Add the flour, baking powder, baking soda, and salt. With the mixer running, slowly stream in the cooled and reduced cider and the buttermilk, mixing until just combined. Do not overmix.
Divide the batter evenly between the cake pans. Bake 30-35 minutes until the center is set and an inserted toothpick emerges with just a few moist crumbs. Let cool in the pans for 10 minutes, then run a knife around the edges to release the layers and flip onto a wire rack. Cool completely.
When the cakes are cooled, make the frosting. In a bowl, whip the cream cheese, butter, caramel, and vanilla on low speed until combined. Add in 4 cups of powdered sugar and mix to combine, then increase the speed to medium high and whip until very light and fluffy. If needed, pour in more sugar 1/4 cup at a time until the frosting is soft and spreadable.
Place one cake layer on a flat plate or cake stand. Frost the top generously, then add the second layer. Frost all the way around the cake until completely covered. If you have extra frosting, feel free to pipe little decorations onto the cake. Finish by swirling some extra caramel into various parts of the frosting.