Prepare Mixing Equipment: Set up your stand mixer with the paddle attachment, or prepare a large mixing bowl with an electric hand beater.
Cream Butter, Sugar & Flavors: Add softened butter and powdered to the bowl and beat on medium-high for 1 minute, scraping down the sides with a spatula. Add the lemon zest, lemon juice, and vanilla, then beat until well combined, about 30 seconds.
Incorporate Flour: Sift over the flour and beat until incorporated, forming a crumbly dough. Bring the dough together with your hands to form a soft dough ball.
Shape Dough: Place the dough on a lightly floured surface. Roll it into a log approximately 30cm (11-12 inches) in length.
Chill: Wrap the dough log in plastic wrap and refrigerate for 1 hour.
Preheat Oven & Line Pan: With 30 minutes left of chill time, preheat the oven to 356ºF (180ºC) fan-forced. Line a baking sheet with parchment paper and set aside.
Slice Cookies: After chilling, remove the dough from the fridge and unwrap it. Slice into rounds approximately 1cm (1/2 inch) thick. Place on the lined baking sheet, leaving a 5cm (2-inch) gap between each.
Bake: Bake for 12-15 minutes, until edges are lightly golden but centers are still pale. Avoid over-baking to maintain the melt-in-your-mouth texture.
Cool: Remove from oven and allow to cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.