Preheat your oven to 350°F (175°C).
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Mix in the lemon zest and vanilla extract.
In another bowl, whisk together the gluten-free flour, baking powder, salt, and poppy seeds. Gradually add to the wet ingredients, mixing until just combined.
Divide the dough in half and shape each half into a log about 12 inches long and 2 inches wide. Place the logs on a baking sheet lined with parchment paper.
Bake for 25-30 minutes, or until the logs are golden brown. Remove from the oven and let cool for 10 minutes.
Reduce the oven temperature to 325°F (165°C). Using a serrated knife, slice the logs diagonally into ½-inch thick slices. Place the slices cut side down on the baking sheet.
Bake for an additional 10-15 minutes, or until the biscotti are crisp and golden. Cool completely on a wire rack before serving.