Step 1: Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan. You can also line the bottom with parchment paper for easy removal.
Step 2: In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, and salt. Set aside.
Step 3: In a separate bowl, whisk together the granulated sugar, vegetable oil, and eggs until the mixture is smooth and well combined.
Step 4: Stir in the finely grated carrots and any optional mix-ins (like crushed pineapple, nuts, or raisins) with a spoon, just until evenly distributed.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Be careful not to overmix the batter; a few streaks of flour are fine.
Step 6: Pour the batter into the prepared cake pan and spread evenly. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean and the top springs back when lightly touched.
Step 7: Let the cake cool in the pan on a wire rack for 10-15 minutes before inverting it onto the rack to cool completely. Do not frost until the cake is entirely cool.
Step 8: For the Cream Cheese Frosting: In a large bowl, beat the softened cream cheese and butter together until light and fluffy.
Step 9: Gradually add the sifted powdered sugar, one cup at a time, beating until smooth after each addition.
Step 10: Mix in the vanilla extract and a pinch of salt. Beat until the frosting is smooth and creamy. If it's too thick, add a tiny splash of milk. If too thin, add more powdered sugar.
Step 11: Once the cake is completely cool, spread the cream cheese frosting evenly over the top and sides of the cake. Decorate with additional chopped nuts or carrot shavings, if desired.