Cream the softened butter and powdered sugar together in a large mixing bowl until light and fluffy, about 2-3 minutes.

Add the vanilla extract and mix until well combined.

In a separate bowl, whisk together the all-purpose flour and salt. Gradually add this dry mixture to the butter mixture and mix until a soft dough forms.

In a small bowl, combine the raspberry jam with the crushed raspberries (if using) and stir until well blended.

On a lightly floured surface, roll the cookie dough into a rectangle about 1/4 inch thick. Spread the raspberry jam mixture evenly over the dough, leaving a small border around the edges.

Starting from one edge, carefully roll the dough into a log. Wrap the log in plastic wrap and refrigerate for at least 1 hour.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

Remove the log from the refrigerator and slice it into 1/4-inch thick rounds. Place the cookies on the prepared baking sheet, spacing them about 2 inches apart.

Lightly sprinkle granulated sugar on top of each cookie and bake for 12-15 minutes, or until the edges are lightly golden.

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