Preheat the oven to 350°F (175°C) and grease two 9-inch round cake pans.

In a bowl, whisk together the gluten-free flour, baking powder, baking soda, cinnamon, and salt.

In a separate large bowl, beat the granulated sugar, brown sugar, and eggs until well combined.

Gradually add the oil to the egg mixture, mixing until smooth.

Fold in the grated carrots, crushed pineapple, and walnuts (if using).

Slowly add the dry ingredients to the wet ingredients, mixing until just combined.

Divide the batter evenly between the prepared cake pans.

Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.

Let the cakes cool in the pans for 10 minutes, then transfer to wire racks to cool completely.

For the frosting, brown the butter in a saucepan over medium heat, then let it cool slightly before mixing with powdered sugar and vanilla.

Once the cakes are completely cool, frost the top of one layer, place the second layer on top, and frost the top and sides of the cake.