• Preheat your oven to 350°F. Grease two 8-inch round baking pans and set them aside. If making cupcakes, grease or line two standard 12-cup muffin tins, and set them aside.
• In a large bowl, place the flour, xanthan gum, baking soda, baking powder, salt, cinnamon and granulated sugar. Whisk to combine well. Add the brown sugar, and whisk again to combine, working to break up any lumps in the brown sugar.
• Create a well in the center of the dry ingredients, and add the oil, eggs, vinegar, and milk, and mix to combine. Add the (optional) pecans and white chocolate chips, and mix until evenly distributed throughout.
• Add the grated carrots to the mixture, and stir until evenly distributed throughout the batter. The batter will be thick, but relatively soft.

To make a cake.

• Divide the batter evenly among the two prepared baking pans, and spread into an even layer in each.
• Place in the center of the preheated oven and bake until the cake is uniformly light brown on top, and beginning to pull away from the sides of the pan rotating the pans once during baking (35 to 40 minutes).
• Remove the pans from the oven from the oven and allow the cakes to cool for at least 10 minutes before transferring to a wire rack to cool completely.

To make cupcakes.

• Fill the wells of the prepared muffin tins about 3/4 of the way full with batter, and shake the pan back and forth to distribute the batter evenly in each well.
• One at a time, place the muffin tins in the center of the preheated oven and bake until a toothpick inserted in the center of the cupcakes comes out with no more than a few moist crumbs attached (about 20 minutes).
• Remove the tin from the oven from the oven and allow the cupcakes to cool in the pan for at least 5 minutes before transferring to a wire rack to cool completely. Repeat with the remaining muffin tin.

Make the frosting.

• While the cakes or cupcakes are cooling, in the bowl of your stand mixer fitted with the paddle attachment (or a large bowl with a handheld mixer), place the cream cheese and butter.
• Beat on medium speed until light and fluffy, about 5 minutes.
• Add the salt, and 3 1/2 cups of confectioners’ sugar. Mix on low speed until the sugar is absorbed. Turn the mixer to high speed and beat until the frosting is thickened and fluffy.
• Add more confectioners’ sugar as necessary to thicken the frosting enough to hold its shape when scooped with a spoon.

To frost a layer cake.

• Turn one of the cooled cakes, top down, onto a serving platter. Spoon about half of the frosting onto the top of the cake and spread into an even layer.
• Top with the second cake, top-down and press to adhere. Spread the remaining frosting on top of the cake and top with more chopped pecans, if desired. To make the cake easier to slice, chill for about an hour in the refrigerator before slicing and serving.

To frost cupcakes.

• Spoon or pipe the frosting onto the cooled cupcakes.