In a medium saucepan, combine the packed chopped strawberries, packed chopped rhubarb, and granulated sugar. Cook over medium heat until boiling, then reduce heat and simmer for about 10-15 minutes until thickened. Spoon dollops onto a tray and freeze until solid, about 1 hour.

Brown the butter in a saucepan over medium heat until golden, then cool slightly. Whisk together flour, cornstarch, baking soda, and salt in a mixing bowl. Beat granulated sugar, brown sugar, egg, and yolk in a stand mixer until frothy. Blend in the cooled butter, vanilla, and cold water.

Gradually mix the dry ingredients into the wet mixture until combined. Fold in half of the frozen jam dollops and chill the dough for 15-20 minutes if needed.

Preheat oven to 350°F (175°C) and line baking sheets with parchment paper. Scoop dough onto sheets, leaving space. Swirl reserved jam dollops on top of each cookie.

Bake for 10-12 minutes until edges are golden and centers are set. Allow to cool on sheets for 5 minutes, then transfer to a wire rack.