Preheat your oven to 350°F and line a baking sheet with parchment paper.
In a large bowl, beat the butter, granulated sugar, and powdered sugar together for 2–3 minutes until light and fluffy.
Add the egg, lemon zest, lemon juice, vanilla extract, and lemon extract (if using). Mix until smooth and fully combined.
In a separate bowl, whisk together the flour, cornstarch, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Scoop large portions of dough (about ¼ cup each), roll into balls, and slightly flatten the tops.
Chill the dough balls for 30 minutes to prevent spreading.
Bake for 10–11 minutes, until the edges are set and the centers are soft and slightly underbaked.
Let the cookies cool on the baking sheet for 5–10 minutes, then transfer to a wire rack and cool completely.
To make the frosting, beat the butter until smooth, then add powdered sugar, raspberry preserves, heavy cream, and salt. Mix until light and fluffy.
Spread the frosting evenly over completely cooled cookies.