Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Toss chopped strawberries with 2 tablespoons sugar and let sit for 10 minutes. Drain excess liquid.
In a bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy.
Add eggs one at a time, then mix in vanilla extract.
Stir in sour cream or Greek yogurt until combined.
Gradually add dry ingredients and mix until just combined.
Fold in strawberries gently. If needed, add cornstarch to absorb extra moisture.
Scoop dough onto prepared baking sheets, spacing cookies 2 inches apart.
Mix crushed shortbread cookies with melted butter and sprinkle over cookie dough.
Bake for 12–14 minutes or until edges are lightly golden.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack.
Dust with powdered sugar or drizzle with white chocolate before serving if desired.