In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the fresh lemon zest, lemon juice, and vanilla extract to the bowl. Mix until well combined.
In a separate bowl, sift together the all-purpose flour, baking powder, baking soda and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms. Be careful not to overmix.
Divide the dough in half and shape each portion into a log, about 2 inches in diameter. Wrap the logs tightly in plastic wrap and refrigerate for at least 2 hours or until firm.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Unwrap the chilled dough logs and roll them in powdered sugar until coated.
Slice the logs into ¼-inch thick rounds and place them on the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 8-10 minutes or until the edges turn just golden.
Remove from the oven and let the cookies cool on the baking sheet for a few minutes, then transfer them to a wire rack to cool completely