For the cheddar cheese pie crust: In a food processor, pulse the flour and salt until well combined. Add the butter and cheese and pulse until small pea-size balls form. Gradually add the ice water, up to 3 tablespoons. Remove the dough from the food processor bowl, fold the dough, wrap with plastic wrap and refrigerate for at least an hour.
Preheat the oven to 325 degrees F. Dust the work space with flour. Roll out the pie dough and cut desired shapes with a cookie cutter. Place the shapes on a baking sheet, brush with water, dust with cinnamon-sugar and bake until golden brown, about 15 minutes.
For the cupcakes: Preheat the oven to 325 degrees F. Line muffin pans with 24 muffin liners. In a medium bowl, whisk the flour, baking powder, baking soda and salt until well combined. In the bowl of an electric mixer with the whisk attachment, add the carrots, beets, oil and granulated sugar and whisk on medium for 1 minute until combined. Add the eggs, one at a time, scraping the bowl as needed. Add the sour cream, lemon juice and lemon zest and mix for about a minute until well combined. With the mixer on low, gradually add the flour mixture just until combined. Then remove from the mixer and scrape by hand. Fill the prepared muffin pans three-quarters full with batter and bake until a toothpick inserted comes out clean, about 24 minutes.
For the frosting: Whip the cream cheese and butter in an electric mixer with the paddle attachment until fully incorporated. With the mixer on low, gradually add the powdered sugar until combined. Add the vanilla and mix until combined. Finally, add the cinnamon and mix until fully incorporated.
For the apple filling: In medium saucepan over medium heat, combine the apples, sugar and 1/8 cup water. Bring to a boil and stir until the water has evaporated and the apples are soft. Add the cinnamon and refrigerate until cool.
To assemble: Use a knife to make a hole out of the center of the cupcakes. Fill with apple pie filling, and then frost with cinnamon cream cheese frosting. Top with a Cheddar cheese shape.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.