Cream together the softened unsalted butter and granulated sugar for about 3 minutes until pale and fluffy. Add the room temperature egg and lemon zest, mixing until combined.

In a separate bowl, whisk together all-purpose flour, cornstarch, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, stirring until a thick dough forms.

Gently fold in the finely chopped fresh raspberries into the dough with a spatula.

Spoon dollops of raspberry jam onto the cookie dough and swirl it through the dough gently.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop mounds of dough onto the prepared baking sheet and bake for 10-12 minutes.

Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack. Dust with powdered sugar and lemon zest before serving.