Preheat oven to 350°F. Grease and flour two 9-inch round cake pans.
In a bowl, whisk flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
In another bowl, beat granulated sugar, brown sugar, eggs, vegetable oil, applesauce, and vanilla until smooth.
Gradually mix dry ingredients into wet ingredients until combined.
Fold in grated carrots and chopped pecans.
Divide batter evenly between the prepared pans. Bake for 30-35 minutes, or until a toothpick inserted comes out clean.
Let cakes cool in pans for 10 minutes, then transfer to a wire rack to cool completely.
For the frosting, beat cream cheese and butter until smooth. Gradually add powdered sugar, vanilla, and salt. Beat until creamy.
For the caramel sauce, melt sugar in a saucepan over medium heat. Stir until golden brown.
Add butter and stir until melted. Slowly pour in heavy cream, stirring constantly. Remove from heat and add vanilla and salt. Let cool slightly.
Place one cake layer on a plate. Spread half the frosting on top. Drizzle with caramel sauce.
Place the second layer on top. Frost the top and sides of the cake. Drizzle with remaining caramel sauce and garnish with toasted pecans.