In a large mixing bowl cream together the butter and sugar until light and fluffy, about 3 minutes.
Add the eggs, vanilla extract, and almond extract. Mix well. At first the mixture will look curdled, but eventually will come together smoothly.
Mix in the flour, almond flour, baking powder, baking soda, and salt. Combine until not flour pockets remain.
Cover and chill the cookie dough for 1 hour or freeze for 30 minutes, stirring the dough halfway through. Preheat the oven to 350°F and line two baking sheets with parchment paper.
Use a ¼ cup measuring cup or cookie scoop to divide up the dough into 12 large balls. Roll the balls until uniform and smooth and place 6 on each baking sheet, evenly spaced apart. Dip a flat-bottomed glass in sugar and press the cookies down slightly. Repeat dipping in sugar, as necessary.
Bake the cookies for 14-16 minutes, rotating the pans halfway through. The cookies are done with the tops are not shiny and just start to crack. Do not overbake. Cool the cookies on the baking sheets as the frosting is prepared.
In a large bowl or stand mixer fitted with paddle attachment, mix together softened butter, powdered sugar, almond extract, and salt.
Add the heavy cream and mix until blended. Once it is fully mixed in, increase the speed to high and beat for 5-7 minutes, scraping down bowl occasionally. The frosting should be very white and fluffy, like a bowl of whipped cream. Add the food coloring and mix again.
Use a large cookie scoop to divide the frosting onto the very slightly warm cookies. Use a small spreader (I used a cheese spreader) to push the frosting evenly on the tops.
Serve at room temperature or refrigerate until well chilled. See recipe notes for storing / freezing tips.
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Storing and Freezing
These are best enjoyed within a day or two of making them. Gluten-free cookies have a tendency to dry out quickly.To keep the frosting and cookies soft, serve at room temperature. Store in an airtight container, with the cookies in a single layer.To enjoy a copycat chilled sugar cookie, store the cookies in the refrigerator and serve cold. Before stacking the cookies in an airtight container, chill the cookies first on a baking sheet so the frosting becomes stable.With all gluten-free cookies, I recommend freezing if not enjoying the same day. Chill the cookies first on a baking sheet so the frosting becomes stable. Then wrap individually in plastic wrap and transfer to a ziplock freezer bag. Freeze up to 6 weeks.Recipe inspired by Cooking With Karli