In a small saucepan melt the butter and then set aside to cool. In a large bowl mix together the flour, baking powder and salt. Set aside.
In a large food processor, add the sugar and lemon zest and process for about 30 seconds or until zest is finely ground. Add the egg, egg yolk, butter, oil, vanilla extract and lemon juice. Process again for about 30 seconds or until mixture is pale yellow and completely incorporated. Add the wet ingredients to the dry ingredients and mix with a wooden spoon until incorporated. Cover the bowl and chill in the fridge for a minimum of 2 hours up to 24 hours.
Place the granulated sugar and icing sugar in two separate small bowls then set aside.
Preheat the oven to 350 degrees F and line two baking sheets with parchment paper. Roll dough into 1 inch balls, toss in granulated sugar first, then generously toss in icing sugar and place on the baking sheets 2 inches apart. Bake one sheet at a time for 12 minutes rotating the sheet halfway through until dough is set and bottoms are golden brown. Let the cookies cool for 5-10 minutes before transferring to cooling racks. Allow to cool completely the store in air tight containers.