Preheat the oven to 175°C (350°F). Line a 20cm x 20cm baking dish with parchment paper, leaving some overhang on the sides.
Mix the gluten free flour, sugar, and salt in a bowl. Add the melted butter and vanilla and mix until a soft dough forms.
Transfer the dough to the prepared pan and press firmly and evenly into the bottom.
Bake for 18–20 minutes, until the edges are lightly browned and the center looks dry and set.
While the crust bakes, whisk together the eggs, sugar, gluten free flour, lemon juice, lemon zest, vanilla, and salt until smooth.
Pour the lemon filling over the warm crust.
Return to the oven and bake for approximately 20 minutes, until the edges are set and the center has a slight wobble.
Allow to cool completely at room temperature, then refrigerate for at least 2 hours.
Lift the chilled bars from the pan, slice into 9 large bars, and dust with powdered sugar just before serving.