Preheat oven to 350°F. Pulse the graham crackers and pecans in a food processor until finely ground. Place in a medium bowl and stir in the butter, sugar and salt.
Press a spoonful of crumb mixture into the bottom of each mini cheesecake tin (the kind with the removable bottoms). Bake until golden brown and slightly firm, 10 to 12 minutes. Don't over-bake or the pecans will begin to burn. Let cool on wire rack. Reduce the oven temperature to 325°F.
MAKE THE CHEESECAKES:
Melt the butter in a medium saucepan over medium heat. Add the carrots and ¼ cup of sugar; cook, stirring often, until the carrots are soft, 3 to 4 minutes. Transfer with the pan juices to a bowl, and let cool.
In a medium bowl, use an electric mixer to beat the cream cheese and remaining ½ cup of sugar on medium speed until fluffy, about 4 minutes. Add the eggs, 1 at a time, scraping down the sides of the bowl as needed. Add the carrots and pan juices, nutmeg, cinnamon, ginger, salt and vanilla, and beat until incorporated. Spoon on top of the crusts to about ¾ full.
Bake until set, about 18 to 22 minutes. Watch closely and pull out of the oven when the cheesecakes are set (touch the tops and make sure they're not jiggly, but firm).
Transfer the pans to a rack and let cool. Refrigerate until ready to add the icing.
MAKE THE ICING:
In a medium bowl, use an electric mixer to beat the cream cheese and butter on medium speed until smooth. Gradually add the powdered sugar and vanilla, beating until smooth.
Place a heaping teaspoonful of icing on top of each cheesecake and spread gently to cover the tops.
If you want to top with the marzipan carrots, see the link in the tips below.
Notes
If preparing this recipe as GLUTEN FREE, sub GF gingersnaps (crumbled) for the graham crackers.
You can always make these without the icing, but it adds a fun and delicious element to the dessert that is unexpected on a cheesecake.