Preheat your oven to 350°F and line a baking sheet with parchment paper.
In the bowl of your mixer, cream together the sugar, oil, eggs, milk, and lemon extract until well combined.
In a separate bowl, whisk together the flour and baking powder.
Add the dry ingredients to the wet ingredients and mix well.
Drop spoonfuls of dough onto the prepared baking sheet.
Bake for 10 minutes at 350°F.
Let the cookies rest on the baking sheet for 2 minutes, then transfer them to a rack and let cool completely.
For the icing, mix the melted butter and heavy cream in a bowl, then stir in the remaining icing ingredients.
Add a few drops of yellow food coloring until you reach the color you like.
Frost the cooled cookies, then let the icing dry and harden.
Garnish with lemon zest.