• Preheat the oven to 325°F
• Add the flour, cornstarch, baking soda, and salt together, whisk to combine, and reserve until needed.
• Using an electric mixer, beat the butter and sugar until well combined. Add the lemon oil, lemon juice, and lemon zest, and mix until well blended.
• Add 1/3 of the flour mixture to the batter and mix at low speed. Slowly add the remaining flour and increase the speed to medium until well blended. The dough will be very soft.
• Cover the dough with plastic wrap and refrigerate for at least 15 to 20 minutes to firm up slightly (this will make the dough easier to handle but you can skip this step and the dough will eventually firm up while it sits at room temperature.)
• Drop 12 rounded tablespoons onto a baking sheet lined with parchment paper. Space the cookies to allow for spreading. With a silicone spatula dipped into flour, or the bottom of a glass, flatten each of the mounds to 1/4 inch thickness.
• Transfer to the middle rack of the oven and bake for 9 to 12 minutes or until the edges begin to turn slightly golden. Remove from the oven and allow to cool 3 minutes on the baking sheet. Sprinkle the cookies with coarse sugar while they are still warm. Transfer the cookies to a wire rack to cool completely. The cookies will get crisp when they completely cool down.

For the lemon icing:

• Place the powdered sugar in a bowl. Add the lemon juice, 1 tablespoon at a time until you get a consistency that is easy to drizzle on the cookies.
• Drizzle the cookies with lemon icing and let the icing dry before storing.