Melt ½ cup of unsalted butter until creamy, then mix with 1 cup of granulated sugar and the zest of one lemon until combined. Add one large egg plus an extra yolk, ¼ cup of vegetable oil, 2 tablespoons of fresh lemon juice, and 1 teaspoon of vanilla extract. Whisk until smooth.

In another bowl, combine 2 cups of all-purpose flour, 1 teaspoon of cornstarch, ½ teaspoon of baking powder, ½ teaspoon of baking soda, and ¼ teaspoon of salt. Stir to mix, then incorporate into wet ingredients until just combined.

Cover the dough with plastic wrap and refrigerate for at least 30 minutes to prevent spreading during baking.

Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop tablespoon-sized dough portions onto the sheet, flattening them slightly. Bake for 12-13 minutes or until edges are golden.

While cooling, prepare the strawberry buttercream by blending ½ cup of softened butter with 1 cup of powdered sugar until smooth. Add ground freeze-dried strawberries, 2 tablespoons of heavy cream, 1 tablespoon of lemon juice, 1 teaspoon of vanilla extract, and a pinch of salt. Mix until fluffy.

Frost cooled cookies with strawberry buttercream and garnish with additional crushed freeze-dried strawberries and lemon zest.