Pre-heat oven to 350°F and line 9-inch square baking pan with parchment paper, leaving a little over-hang.
In a medium bowl, whisk together the gluten-free all-purpose flour, xanthan gum, salt, baking powder, and baking. Set aside.
Use a stand mixer or hand mixer to cream together 1/2 C butter and the granulated sugar until light and fluffy. Scrape down the bowl and beat in the egg and vanilla extract. Add the dry ingredients and mix until combined, scraping the bowl as needed.
Transfer the dough to the prepared pan and spread evenly in the pan. The dough will be sticky so it might help to press the dough in with well-floured hands or a spatula sprayed with non-stick spray.
Bake for 22-25 minutes.
Cool in the pan on a wire rack. Cool completely before frosting.
To make the frosting, beat together ½ cup butter, powdered sugar, and a pinch of sea salt on low. Increase speed to medium and beat for 3 minutes. Add vanilla and whipping cream and food coloring (if using) and beat for another minute.
Use the parchment paper to lift the sugar cookie bars from the pan. Evenly spread frosting over the completely cooled bars and top with sprinkles if using. Makes 16 bars.
If desired, double the frosting for a thicker layer.
Store in an air-tight container up to 3 days at room temperature.