Begin by melting 1 cup of unsalted butter in a medium saucepan over low heat. Once fully melted, remove from heat and allow the butter to cool slightly for about 5 minutes.

In a large mixing bowl, combine 1 cup of granulated sugar and the zest of 2 lemons. Use your fingers to rub the lemon zest into the sugar, releasing the fragrant oils.

Whisk the cooled melted butter, 1/4 cup vegetable oil, 2 large eggs, 2 egg yolks, 1/4 cup fresh lemon juice, and 2 teaspoons of vanilla extract into the sugary lemon zest mixture.

In a separate bowl, whisk together 2 cups of all-purpose flour, 1 teaspoon of cornstarch, 1 teaspoon of baking powder, 1/2 teaspoon of baking soda, and 1/4 teaspoon of salt.

Gradually add this dry mixture to the wet ingredients, mixing gently until fully incorporated. Cover the cookie dough with plastic wrap and refrigerate for at least 30 minutes.

While the cookie dough chills, preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.

Once the dough is chilled, use a cookie scoop (about 3 tablespoons) to portion the dough onto the prepared baking sheets.

Place the baking sheets in the preheated oven and bake the cookies for 12-13 minutes.

While the cookies cool, make the frosting by grinding 1/2 cup of freeze-dried strawberries into a fine powder.

Once the cookies have completely cooled, generously frost each with the strawberry buttercream.