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, preheat the oven and prep pans just before rolling out dough and cutting shapes.
Pulverize the freeze dried strawberries to a fine powder using a food processor or blender. (If you do not have either of these, use a mortar and pestle or something similar.)
In a medium sized bowl, whisk together flour, freeze dried strawberry powder, salt, and cornstarch. 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 granulated sugar, 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, and beat until incorporated. Add in extracts and mix them in as well, once again scraping the bowl 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, press the dough into a 1 inch thick disk or square on saran wrap, and then wrap. Place the dough in the fridge for two hours.
Lightly flour your work surface and the top of the dough, and roll your dough out until it's 3/8 inch thick. (Rolling pin with thickness rings linked in post) 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. Dip cookie cutter in flour every other cut to prevent sticking as well.
Cut out as many cookies as you can from your first roll out, and place them on to the prepared baking sheets with 1" of space minimum. Squish together the scraps without overworking.
Continue rolling the dough, cutting shapes, and squishing together scraps until no dough remains. (Try not to knead the dough together when working with the scraps, but instead squish it and pull the seams to the backside. 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 10-13 minutes, or until the tops of the cookies are no longer shiny, but instead are an eggshell/matte finish. Do not bake cookies to the point of browning because it will dry them out. (You can bake multiple trays at a time, but run the risk of cookies baking less evenly. If you choose to do multiples, make sure to rotate trays around halfway through. If you roll the cookies thinner than 3/8, you will also want to bake them a bit less, and should start checking around 7-9 minutes)
Allow cookies to cool completely before frosting. Store in an airtight container.