If using the no chill method, preheat oven to 350° and line two baking pans with silicone mats (or parchment paper). If you plan on chilling the dough (which I recommend), preheat the oven and prep pans just before rolling out dough and cutting shapes.
In a medium sized bowl, combine the lemon zest and the granulated sugar. Rub the zest in to the sugar with your fingers for 1-2 minutes to release the lemon's oils and enhance the flavor. Set aside.
In a medium sized bowl, whisk together flour, salt, and cornstarch. (See notes about measuring dry ingredients correctly to avoid dry cookies) Set aside.
Beat the butter in a large sized bowl using an electric mixer until butter has begun to evenly spread around the sides. Add in cream cheese and mix just until combined. Scrape down the bowl, and repeat.
Add in the lemon zest granulated sugar mixture, and mix until well combined scraping down the sides of the bowl and beater as you go. Do NOT continue mixing to make it light and fluffy.
Mix in the egg and egg yolk, fresh lemon juice, vanilla extract, and lemon oil and beat until incorporated. Once again, scraping the bowl as needed to ensure even mixing.
With the mixer on a low speed, slowly add in the flour mixture, and allow dough to come together until no dry ingredient streaks are remaining. Stop the mixer, scrape down the bowl and beater, and beat for another several seconds on medium speed.
If chilling, divide the dough in two pieces and press each half into a 1 inch thick disk or square, and then wrap in saran wrap. Place the dough in the fridge for two hours.
Lightly flour your work surface and your dough, and roll out half of your dough out until it's 3/8 inch thick. Every several rolls or so, pick the dough up and swipe your hand across the back of it and the counter to check for adequate flour amounts to prevent sticking. Use minimal flour, just enough to prevent dough from sticking to the counter and rolling pin. Remove dough buildup on cookie cutter and dip it in flour as needed to prevent sticking.
Cut out as many cookies as you can from your first roll out, and place them on to the prepared baking sheets with a minimum of 1" of space. Squish together the dough scraps in saran wrap and place them back in the fridge while you roll out the second half of the dough.
Once you've cut shapes from the second half of rolled out dough, squish together remaining scraps of dough from both halves to re-roll. Continue rolling the dough, cutting shapes, and squishing together scraps until no dough remains. (Try not to knead the dough too much when working with the scraps, but instead squish it or press it together. The goal is to work the dough the least amount possible.)
For the most even bake, bake one tray at a time on the center rack for 10-15 minutes, or until the tops of the cookies are no longer shiny, but instead are an eggshell/matte finish. Remove at any sign of browning especially. (If you choose to bake multiple trays at a time, make sure to rotate trays halfway through. If you roll the cookies thinner than 3/8 or do small shapes, they will need less time to bake)
Allow cookies to cool completely before frosting. Store in an airtight container.