Preheat oven to 350 degrees. In a mixing bowl, whisk together flour, baking soda, cinnamon, nutmeg and salt, set aside. In a large mixing bowl, using an electric hand mixer on medium speed, blend together butter, sugar and applesauce until well blended and fluffy, about 1 minute. Add in eggs one at a time mixing until combine after each addition.
Blend in lemon juice and vanilla. With mixer on low speed, slowly add dry ingredients and mix just until combine. Fold in finely grated apples (as well as the juice of the grated apples). Divide batter among paper lined muffin cups filling each cup about 1/2 full.
Bake cupcakes in preheated oven 17 - 19 minutes until golden brown and toothpick inserted into center of cupcake comes out clean. Allow to cool completely then frost with Caramel Frosting. Just before serving, drizzle cupcakes with leftover caramel sauce and sprinkle lightly with sea salt. Store cupcakes in an airtight container.
Fluffy Caramel Frosting
In the bowl of an electric stand mixer fitted with paddle attachment, whip butter on medium-high speed until pale and fluffy, about 3 - 4 minutes. Add powdered sugar and blend on low speed until mixture comes together. Add caramel sauce and vanilla and whip on medium-high speed until light and fluffy about 3 - 4 minutes.
Gather all of your ingredients and have them nearby ready to add to the mixture as needed. In a heavy-bottomed 3 quart saucepan, heat sugar and water over moderately high heat whisking constantly to dissolve sugar. Once mixture reaches a boil, stop whisking and allow mixture to boil until it reaches a dark amber color, carefully swirling pan occasionally.
Once mixture reaches a dark amber color, immediately add butter and whisk until butter has melted then immediately remove from heat. Wait 3 seconds then carefully pour in cream and immediately whisk to combine (it will bubble vigorously). Whisk until mixture is smooth. Allow caramel to cool several minutes then pour into a glass jar to cool completely.