Preheat oven to 350°F. Line 12 cupcake molds with cupcake liners. Set aside.
In a standing mixer fitted with a whisk attachment, mix the sweet potato puree, sugar, oil, eggs, and vanilla extract until well-combined. Add in the flour, baking powder, baking soda, spices, and salt, mixing only until combined.
Pour batter evenly into cupcake liners. Bake for 15 minutes, then allow to cool completely before frosting.
To make the frosting, cream the butter in a standing mixer fitted with a whisk attachment for about 1 minute. Add in the cream cheese, beating for another minute. Add in powdered sugar, vanilla, and salt, beating until the frosting is nicely whipped, about 30 seconds more.
Place 3 tablespoons of frosting over each cupcake, and use the back of a knife to smooth it out. Drizzle on caramel and top with crushed pecans!