In a small bowl, beat the softened cream cheese and powdered sugar together until smooth. Scoop into tablespoon-sized portions, place on parchment paper, and freeze until firm.

Line baking sheets with parchment paper and preheat oven to 350°F (175°C).

In a medium bowl, whisk together flour, cornstarch, baking powder, baking soda, and salt.

In a large bowl, use a mixer to cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Mix in the egg, egg yolk, and vanilla extract until combined.

Gradually add the dry ingredients and stir until just combined.

Gently fold in the diced fresh strawberries, taking care not to crush them.

Scoop large portions of cookie dough (about 2 tbsp each) and press a small indentation in each. Place a frozen cream cheese portion into the center, then cover with another small portion of dough, pinching to seal.

Place cookies on prepared sheets and bake for 12–15 minutes until edges are set and centers are soft.

Let cookies cool on the baking sheet until firm enough to transfer to a cooling rack.