In the bowl of a stand mixer fitted with a dough hook, combine the gluten-free flour, granulated sugar, instant yeast, xanthan gum (if using), and salt. Add the melted butter, warm milk, eggs, vanilla extract, and lemon zest. Mix on medium speed until a smooth dough forms. The dough will be sticky. Transfer the dough to a lightly floured surface and knead briefly to form a ball. Place in a greased bowl, cover with a damp cloth, and let rise in a warm place for 1 hour, or until doubled in size. Preheat your oven to 350°F and line a baking sheet with parchment paper.
Roll out the risen dough into a rectangle, about 1/4-inch thick. Spread the softened butter over the dough, leaving a small margin at the edges. Mix the brown sugar and cinnamon together and sprinkle evenly over the butter.
Starting at the long edge, roll the dough tightly into a log. Form the log into a circle on the prepared baking sheet, pinching the ends together to seal. Bake for 30 minutes, or until golden brown. Let cool slightly on a wire rack. For the icing, mix the powdered sugar, milk (or water), and vanilla extract until smooth. Adjust the consistency with more liquid or powdered sugar as needed.
Drizzle the icing over the warm cake. Immediately sprinkle the colored sugar in alternating bands of purple, green, and gold around the cake. Serve and don’t forget to hide a small, oven-safe figurine inside for someone to find!