In a medium bowl, whisk together the gluten-free flour blend, baking powder, and salt. Set aside.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3 minutes.
Beat in the egg, vanilla extract, lemon zest, and 2 tablespoons of lemon juice until just combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until a soft dough forms. Do not overmix.
If making cut-out cookies, wrap the dough in plastic wrap and chill for at least 1 hour. If making drop cookies, proceed to the next step.
For drop cookies: Drop rounded tablespoons of dough onto baking sheets lined with parchment paper, spacing them 2 inches apart.
For cut-out cookies: Roll the chilled dough between two sheets of parchment paper to 1/4 inch thickness. Cut into desired shapes and place on prepared baking sheets.
Bake drop cookies at 350F (175C) for 9 to 11 minutes, or until the edges are set. Bake cut-out cookies for 8 to 10 minutes. The centers should look slightly soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Prepare the glaze: Whisk together the powdered sugar and 2 tablespoons of lemon juice until smooth. Add more juice, a few drops at a time, if needed to reach a drizzling consistency.
Drizzle or spread the glaze over the cooled cookies. Allow the glaze to set before serving.
Notes
Use a gluten-free flour blend that already contains xanthan gum for the best texture.
For a stronger lemon flavor, add 1/4 teaspoon of lemon extract along with the vanilla.
If the dough is too sticky for rolling, chill it longer or add 1 to 2 extra tablespoons of gluten-free flour.