For the Frosting:
Stir sugar and water together in a small pot and bring to a boil over medium-high heat. (You can stir it up until the sugar dissolves but then DO NOT STIR while it boils or else it will form crystals). Let it boil for 5-6 minutes or until it starts to turn a light caramel brown color. Remove from heat and slowly stream in the cream while stirring. Stir in the vanilla. Let it cool to room temperature (about 30 minutes).
Meanwhile, make the cupcakes. (This is also when I take the butter out of the fridge for the frosting.)
Once the caramel is cool, in a standing mixer, use the paddle attachment to beat the butter and salt together for 3 minutes at medium speed until light and fluffy. Add the sugar and mix it in starting with a low speed. Add half of the caramel (reserve the rest for drizzling) and beat for 2 minutes on medium speed until light and fluffy (scrape the sides of the bowl as needed).
Place frosting in a piping bag fitted with a star tip and pipe onto cooled cupcakes. Drizzle with caramel and serve.
For the Cupcakes:
Preheat the oven to 350 degree F and line a muffin tin with 12 cupcake paper liners.
In a mixing bowl, combine flour, baking powder, cinnamon, salt, and ginger together. Set aside.
In the bowl of a standing mixer beat butter and sugars together until light and fluffy. Mix in the egg and vanilla. Mix in the flour mixture a little at a time until just combined and then add the buttermilk and mix until combined. Fold in the shredded apple.
Spoon batter into cupcake liners filling them 3/4 full (about 1/4 cup). Bake for 22-25 minutes or until toothpick comes out clean.
Let cupcakes cool for a few minutes in the tin and then remove onto a rack to cool completely before frosting.