Preheat oven to 350 degrees. In a large stand mixer fitted with a paddle attachment, mix sugar with butter and shortening until creamy. Throughout the mixing process, scrape the sides of the bowl as necessary with a spatula.
Add eggs and beat well, followed by the sour cream and vanilla extract. Mix on medium speed until the batter is smooth and free of lumps.
Next, add the salt, baking soda, baking powder, and gluten-free flour one cup at a time, mixing after each addition until fully incorporated.
Once a dough has formed, cover the mixing bowl with plastic wrap. Chill in the refrigerator for 30 minutes to overnight.
Remove the chilled cookie dough from the refrigerator. Using your hands, shape the batter into dough balls. Roll each ball in a small bowl of granulated sugar until the surface is completely coated in sugar.
Place 12 dough balls on an ungreased cookie sheet. Using the back of a teaspoon or your thumb, firmly press the center of each cookie, to hold the jam. Next, spoon jam into each thumbprint/indent, about 3/4 of a teaspoon.
Bake for 12-15 minutes or until golden brown and the jam is set. Allow the cookies to rest on the cookie sheet before transferring them to a cooling rack to glaze.
While the thumbprint cookies cool, prepare the vanilla glaze. In a medium bowl, whisk together powdered sugar and milk. For a thicker glaze, add more powdered sugar. For a thinner glaze, add more milk to thin it.
When the cookies have slightly cooled, drizzle the vanilla glaze on the tops. Enjoy!