In a small bowl, combine the sugar and lemon zest by rubbing the mixture between your fingers. Combine it until it resembles damp sand.
In another small bowl, combine the oat flour, baking powder, baking soda, salt, and poppy seeds. Whisk the mixture with a fork.
With a mixer in a large bowl, beat the butter and sugar/lemon zest mixture until creamy and light. Add the egg, lemon juice, and vanilla. Mix at slow/medium speed, scraping down the sides of the bowl as necessary.
Add the flour mixture into the wet ingredients and mix at a slow speed or stir until just combined. Cover the dough with plastic wrap and place into the fridge for 30 minutes (or longer).
15 minutes before you’re ready to bake, preheat the oven to 350°F or 180°C.
Line a baking sheet with parchment paper. Remove the dough from the fridge after at least 30 minutes. Use a tablespoon sized spoon or cookie scoop to scoop the dough onto the baking sheet. Leave about 2 inches between them.
Bake for 10 minutes. Let the cookies cool for 3 minutes on the baking sheet, then move them with a spatula to fully cool on a cooling rack (or just eat them warm!)