Make the crumble topping: In a medium bowl, whisk together flour and sugar. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Set aside.
Make the cookie dough: In a large bowl, whisk together flour, baking soda, and salt. In a separate bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy. Beat in the vanilla and egg.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Drop rounded tablespoons of cookie dough onto ungreased baking sheets. Make a well in the center of each cookie and fill with raspberry jam.
Sprinkle the crumble topping over the jam.
Bake for 12-15 minutes, or until the edges are golden brown.
Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.
Notes
Store cookies in an airtight container at room temperature for up to 3 days.