In a medium bowl, whisk together the gluten-free flour, almond flour, cornstarch, salt and cinnamon.
In the bowl of a stand mixer fitted with a paddle attachment, or using a hand mixer, cream together the butter, granulated sugar and brown sugar on medium-high speed until light and fluffy, about 2-3 minutes.
Add the vanilla and beat until smooth, about 1 minute. 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.
Divide the dough into two discs and wrap each one tightly in plastic wrap. Refrigerate for at least 1 hour, or up to 2 days. (If chilling for more than a few hours, let the dough sit at room temperature for 30 minutes before rolling.)
Line large baking sheets with parchment paper or silicone baking mats.
On a lightly floured surface, roll out the chilled dough to ⅛-inch thickness. Cut the dough into 2½-inch circles (I like to use cookie cutters with scalloped edges).
Use a small heart- or star-shaped cookie cutter to cut designs in the center of half of the cookies. (Or you can use this linzer cookie cutter set!)Use a thin spatula to place the cookies with cutouts on a separate baking sheet from the ones without cutouts to ensure even baking. Freeze the cookies on the baking sheet for 15 minutes. Preheat the oven to 350°F.
Bake the cookies for 9-11 minutes, until the edges are lightly golden.
Remove from the oven and cool on the baking sheets for 10 minutes. Transfer to a wire rack to cool completely.
Dust the cookies with cutouts with powdered sugar. Top the remaining cookies with 1 teaspoon of jam, spreading it slightly. Top with the sugar-dusted cookies.