In a mixing bowl, cream together butter, cream cheese, granulated sugar, and brown sugar until light and fluffy.
Add eggs one at a time, then mix in vanilla extract, lemon extract, lemon zest, and lemon juice.
In a separate bowl, whisk together flour, cornstarch, baking soda, and salt. Gradually add dry ingredients to the wet mixture until just combined.
Fold in freeze-dried strawberries and strawberry extract. If using, gently fold in fresh strawberries.
Chill dough for at least 30 minutes (optional but recommended).
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone mats.
Scoop dough onto baking sheet, spacing about 2 inches apart.
Bake for 9–11 minutes, until edges are set and centers look slightly underbaked.
Let cool on pan for 5 minutes before transferring to a cooling rack.
(Optional) Top with strawberry lemon glaze or use buttercream to make sandwich cookies.