Whisk the eggs, applesauce, sugar, oil, and, vanilla extract together in a medium bowl.
Whisk the flour, baking powder, baking soda, salt, and spices together in a separate bowl.
Add the dry ingredients into the bowl with the wet ingredients and whisk until just combined, then use a spoon or scoop to fill each cupcake liner ⅔ full with the batter.
Select the Preheat function on the COSORI Air Fryer, adjust temperature to 320°F, then press Start/Pause.
Place the cupcakes into the air fryer basket.
Set temperature to 320° and time to 12 minutes, then press Start/Pause.
Remove the cupcakes when done and let cool.
Place the granulated sugar into a saucepan over medium heat and cook, stirring constantly with a rubber spatula. When the sugar has melted and turned into a light brown syrup, lower the heat slightly and stir in the butter immediately, being careful because the butter will cause the sugar to spit and sputter slightly.
Continue stirring and whisk in the cream. The cream will cause the mixture to boil and bubble, as it is significantly colder. Stop stirring and boil the mixture for 1 minute, then stir and remove from the heat and stir in the salt. Whisk until smooth and then let cool slightly.
Place the remaining 1 cup butter and vanilla extract into the bowl of a stand mixer fitted with the paddle attachment and beat until smooth. Add the powdered sugar in 1 cup at a time, beating until smooth between each addition.
Add in ½ cup of the cooled but still liquid salted caramel and continue beating on high until the buttercream is completely smooth and lump-free. Transfer the buttercream into a piping bag fitted with a tip.
Pipe the buttercream onto each cooled cupcake and drizzle extra salted caramel over the top, then serve.