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

In the bowl of a stand mixer fitted with a paddle attachment, or using a hand mixer, cream together the butter and sugar on medium-high speed until light and fluffy, about 2-3 minutes.

Add the eggs and vanilla and mix until well-combined. Scrape down the sides and bottom of the bowl.

With the mixer running on low, slowly add the dry ingredients to the wet ingredients and mix until well-combined. Scrape down the sides and bottom of the bowl, then mix again until fully incorporated.

Scoop ⅔ of the cookie dough (about 530g) into a bowl. Cover and let sit at room temperature while you prepare the cut-outs.

Add 2-3 drops of food coloring to the remaining dough in the mixing bowl. Mix to evenly combine.

On a lightly floured piece of parchment paper, press the colored dough into a ½-inch disc. Freeze the disc for 30 minutes. (This helps the cut-outs hold their shape.)

Remove the disc from the freezer and use a small cookie cutter (about 1½ inches across) to cut out the shapes. Lightly dip your finger in water and dab it onto the floured side of a cut-out, then press another cut-out, flour-side-up, on top. This helps them stick together—just be careful not to use too much water! Repeat with the remaining cut-outs, stacking them to form a log about 10 inches long.

Cover the log and freeze for at least 2 hours until completely solid. (If you’re freezing the log longer than 2 hours, refrigerate the remaining plain dough. Let the plain dough sit at room temperature for at least 30 minutes before using.)

Divide the remaining plain dough into six pieces and roll each one into a 9- to 10-inch cylinder, about the same length as the cut-out log.

Remove the cut-out log from the freezer and arrange the plain dough logs evenly around it, making sure to press them in well to avoid any gaps. Roll the dough-covered log on a lightly floured surface until smooth.

Wrap the log tightly in plastic wrap or parchment paper and refrigerate for at least 30 minutes, or up to 3 days.

Preheat the oven to 350°F. Line large baking sheets with parchment paper or silicone baking mats.

Slice the dough into ¼-inch rounds and place on the prepared baking sheets, about 2 inches apart.

Bake for 10-12 minutes, until the edges are set but the centers are still soft.

Remove from the oven and cool on the baking sheets for 5 minutes. Transfer to a wire rack to cool completely.