Cream butter and sugar together on medium speed for about 3 minutes until pale and fluffy.

Add egg and lemon zest, mixing on low speed until well combined.

In a separate bowl, whisk together flour, cornstarch, baking soda, and salt. Gradually mix into the wet ingredients until just combined.

Gently fold in chopped raspberries without overmixing.

Drop raspberry jam in dollops, then swirl through the dough for marbling.

Preheat oven to 350°F (175°C). Scoop dough onto a lined baking sheet, spacing 2 inches apart. Bake for 10-12 minutes until golden.

Cool cookies on the baking sheet for 5 minutes, then transfer to a wire rack. Dust with powdered sugar before serving.