In a medium bowl, whisk together the gluten-free flour blend, baking powder, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar with an electric mixer until light and fluffy, about 3 minutes.
Beat in the egg, egg yolk, lemon zest, lemon juice, and vanilla extract until just combined. Scrape down the sides of the bowl.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until a soft dough forms. Do not overmix.
Divide the dough in half, flatten each half into a disk, wrap in plastic wrap, and chill in the refrigerator for at least 1 hour.
Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
On a surface lightly dusted with gluten-free flour, roll out one disk of dough to about 1/4-inch thickness. Cut out desired shapes using cookie cutters.
Place the cutouts onto the prepared baking sheets.
Bake for 9 to 12 minutes, depending on the size, until the edges are set but the centers still look slightly soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
While cookies cool, prepare the glaze: Whisk together the powdered sugar and 2 tablespoons of lemon juice until smooth. Add more lemon juice, 1 teaspoon at a time, if the glaze is too thick.
Once cookies are fully cool, drizzle or dip the tops in the lemon glaze. Let the glaze set before serving or storing.
Notes
For a dairy-free option, substitute the butter with a high-quality dairy-free butter stick.
If you prefer softer centers, slightly underbake the cookies by 1 minute. For crispier edges, bake for 1 minute longer.
Store cooled, glazed cookies in an airtight container at room temperature for up to 4 days.