01 - Preheat the oven to 350°F. Line two baking sheets with parchment paper.
02 - In a medium mixing bowl, whisk together all-purpose flour, baking soda, and salt. Set aside.
03 - In a large bowl, beat the softened butter, vegetable oil, and granulated sugar using an electric mixer until light and fluffy.
04 - Add eggs one at a time, mixing thoroughly after each addition. Mix in lemon zest, lemon juice, and vanilla extract until combined.
05 - Gradually add the dry ingredients to the wet mixture, mixing just until incorporated.
06 - Gently fold in diced fresh strawberries until evenly distributed throughout the dough.
07 - Using a tablespoon or cookie scoop, drop mounds of dough onto prepared baking sheets, spacing each about 2 inches apart.
08 - Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden.
09 - Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
10 - In a small bowl, whisk together powdered sugar, lemon juice, lemon zest, and optionally freeze-dried strawberries until smooth.
11 - Drizzle the glaze over the cooled cookies and allow it to set before serving.