Place water and granulated sugar in a saucepan and bring to a boil, stirring occasionally.
Lower stovetop temperature to simmer and add the pineapple pieces. Simmer for 30 minutes.
Turn off the heat and let pineapples sit in the pot for 10 minutes. Remove after 10 minutes with a slotted spoon and place on parchment or wax paper. Let cool completely.
Preheat oven to 350°.
Toss pineapple pieces in granulated sugar and place on baking pan, ensure pieces are not touching each other.
Bake for 10 - 15 minutes, or until sugar is fully melted and the pineapple is just beginning to brown. Cool before using in cupcakes.
Cupcakes
Preheat oven to 350°
Place cupcake liners in a cupcake pan.
Combine flour, sugar, cinnamon, baking powder, baking soda and salt in a bowl.
In another bowl, place shredded carrots and applesauce. Stir to combine.
Add eggs and oil to the carrot/applesauce mixture and stir well to combine.
Place ½ of dry ingredients into mixing bowl and stir to combine.
Place remaining ½ of dry ingredients into mixing bowl and stir to combine.
Optional: add 1 cup of raisins, nuts or any other desired item.
Fill the cupcake liners ⅔ full with the batter.
Bake 18 - 22 minutes, or until the cupcakes are fully risen and a toothpick inserted in the center of a cupcake comes out clean.
Place cupcake pans on a rack and cool completely.
Cream Cheese Icing
Place softened cream cheese and butter in the bowl of a stand mixer fitted with the paddle attachment (a hand mixer may also be used).
Mix cream cheese and butter on medium speed until no lumps remain.
Add powdered sugar and ground cinnamon, Begin mixing on low speed and gradually increase speed to medium-high. Continue to mix for 3 to 4 minutes.
Assemble Cupcakes
Using an apple corer or knife, remove a small piece of each cupcake from the center (approximately ⅓"). Place candied pineapple in each hole.
Top each cupcake with cream cheese icing and sprinkle a few pieces of the candied pineapple on each cupcake.