Preheat your oven to 350 degrees. Line 2 (or 4 if you have) 11x13 inch baking sheets with parchment paper.
In a large bowl beat the butter and sugar until light and creamy, about 2 minutes. Add the egg, lemon zest, lemon juice and, if using, the lemon oil and food coloring and beat to combine.
Add the flour, baking powder and sea salt and beat until just combined.
Scoop the cookie dough using a small ice cream scoop (about 2 tablespoons) and roll the dough into balls. Press the dough down slightly using your fingers. Bake, 2 sheets at a time, for 12 minutes, or until lightly browned at the edges. Remove from the oven and let cool completely. NOTE: if you only have 2 cookie sheets, make sure the ones coming out of your oven are completely cool before you add the remaining cookie dough.
While the cookies are cooling, prepare the frosting. Beat the frosting ingredients together in a medium-sized bowl until well combined.
When the cookies are cool, top them with the frosting. You can add a little lemon zest or a few sugar sprinkles if you'd like.