Preheat oven to 375°F (190°C) and line two baking sheets with parchment paper (or silicone mats), set aside.
Combine butter and sugar in a large bowl and beat until creamy. Whisk in the egg, lemon zest, lemon oil, vanilla and salt, beat until combined. Add the flour and sprinkle baking powder all over, then mix until the dough comes together. It should be smooth, with no dry patches, and soft.
Scoop the dough into 28 pieces, roll them into balls. Roll each one in granulated sugar, place on baking sheets and press flat. You want them to look like medallions, about 1/4 inch (0.5 cm) thick. As the dough is soft, you can shape it at the sides to make perfect circles.
Bake cookies for 8-9 minutes, until golden brown at the edges. Remove from the oven and let cool completely.