Apple Pie Cookie with Salted Caramel Frosting

For the cookies:
Remove apple cores, and finely dice apples. Place in a saucepan with water and the juice from the lemon. Remove the peel from the lemon in large chunks and add that to the apples. Cook over medium heat a few minutes until mostly soft, but still slightly crisp. Remove from heat, drain water, remove lemon peel pieces, and set aside.

Cream butter and sugar, add egg and mix well. Add salt, soda, and spices, and mix well.

Add buttermilk alternately with flour, mixing just until combined. Fold in apple pieces.

Drop by spoonfuls onto baking sheet and bake at 375ºF for 9-12 minutes.

For the frosting:
Melt butter over medium heat. Add sugar and cream and bring to a boil. Remove from heat and let cool for a few minutes. Mix in vanilla and powdered sugar. (To ensure a smooth frosting, you may want to sift the powdered sugar.)

Frost cooled cookies, and quickly garnish with coarse sea salt.