In a medium saucepan, combine strawberries, rhubarb, sugar, and lemon juice. Bring to a boil, cover, and simmer for 10 minutes. Uncover and cook for 3-5 minutes until thick. Pour onto parchment-lined sheet and freeze for 30 minutes.

Brown the butter in a saucepan over medium heat for 3-4 minutes until nutty and golden. Allow it to cool for 30 minutes. Preheat the oven to 350°F (175°C) and line baking sheets with parchment.

In a large bowl, combine flour, cornstarch, baking soda, and salt. Whisk until blended to create the cookie dough base.

In a stand mixer, mix the sugars, egg, and yolk on medium speed until frothy. Add cooled brown butter, vanilla extract, and cold water. Mix until smooth and creamy.

Slowly incorporate the dry ingredients into the wet mixture. Fold in half of the frozen jam, creating swirls in the dough. The mixture should be thick.

Scoop rounded mounds of dough onto prepared baking sheets, spacing 2 inches apart. Swirl remaining jam into the tops. Chill in the fridge for 15 minutes if warm.

Bake in preheated oven for 10 minutes. Bang the baking sheet on the stovetop three times, then continue baking for an additional 4-5 minutes until edges are set.

Let cookies cool on sheets for 10 minutes, then transfer to a wire rack to cool completely before serving.