• Line a rimmed baking sheet with unbleached parchment paper and set it aside.

Make the cookies.

• In a small bowl, place the flour, xanthan gum, baking soda, salt, cinnamon, and oats, and whisk to combine well. Set the bowl aside.
• In the bowl of a stand mixer fitted with a paddle attachment or a large bowl with a hand mixer, place the granulated sugar, brown sugar, butter, shortening, egg, and vanilla, and beat to combine well.
• Add the dry ingredients, and mix to combine. The cookie dough will be thick but quite soft and sticky.
• Scoop the dough into portions about 1 1/2-tablespoons each, using a spring-loaded ice cream scoop or two spoons, and place the mounds close together on a prepared baking sheet.
• Place the pieces of raw dough on the baking sheet in the freezer for at least 30 minutes, or until the dough is firm enough that it is barely sticky to the touch.
• Remove the dough from the freezer, and roll each piece of dough into a round between the palms of your hands. (See Recipe Notes)
• When you’re nearly ready to bake the cookies, preheat your oven to 375°F.
• Line rimmed baking sheets with unbleached parchment paper, and place frozen balls of cookie dough on the baking sheet about 2-inches apart from one another.
• Place the baking sheets, one at a time, in the center of the preheated oven and bake for about 10 minutes, or until lightly golden brown around the edges and an even thickness.
• The cookies may still seem wet in the very center.
• Remove them from the oven and allow to cool until firm on the baking sheet before transferring to a wire rack to cool completely.

Make the glaze.

• In a medium-sized bowl, place the confectioners’ sugar.
• Add the lemon juice and 1 tablespoon of water, and mix until smooth. It will form a very thick paste.
• Add a bit more water, and mix until smooth and well-combined.
• The icing should be bright white and opaque but thickly pourable. If you’ve added too much water, balance it by mixing in more sugar. It’s much easier to thin with a few drops of water than to thicken with more sugar, though, so proceed carefully.
• Working with one completely cooled cookie at a time, turn over the cookie, and hold it around the edges with the tips of your fingers.
• Dip the top of the cookie into the icing, without immersing the cookie. Allow the extra icing to drip off.
• Place, icing side up, on a flat surface.
• Continue with the rest of the cookies.
• The icing will become firm at room temperature, but thicker spots of icing may still be soft underneath the very top layer.