Combine the chopped strawberries and sugar in a small saucepan over medium heat and cook for about 10 minutes, stirring often, until the strawberries break down and the mixture becomes syrupy.

Stir the cornstarch and water together in a small bowl, add it to the strawberry mixture, and cook for 1 more minute until very thick, then remove from heat and let cool completely.

Preheat the oven to 350°F and line a baking sheet with parchment paper.

Whisk together the flour, baking powder, and salt in a medium bowl and set aside.

Beat the butter and sugar together in a large bowl until light and fluffy.

Add the egg and vanilla and mix until fully combined.

Gradually mix the dry ingredients into the butter mixture until a soft dough forms, adding milk if needed to keep the dough from becoming dry.

Spoon about 1 tablespoon of the cooled strawberry jam over the dough and gently fold it in so streaks of jam remain. Add in more jam as needed.

Scoop the dough into tablespoon-sized portions, roll into balls, and roll each ball in granulated sugar.

Place the dough balls on the prepared baking sheet and bake for 10 minutes, until the edges are set but the centers are still soft.

Allow the cookies to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.