Preheat the oven to 325°F (163°C). Line a baking sheet with parchment paper.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 3 to 4 minutes.
Add the vanilla extract and mix until combined.
Gradually add the all-purpose flour and salt to the butter mixture. Mix on low speed until the dough comes together and no flour streaks remain.
Turn the dough out onto a lightly floured surface and knead gently to form a smooth dough.
Roll the dough out to about 1/4 inch thickness.
Use a cookie cutter or knife to cut the dough into desired shapes (about 24 cookies). Place the cookies on the prepared baking sheet, spacing them about 1 inch apart.
Bake the cookies in the preheated oven for 18 to 20 minutes, or until the edges are lightly golden.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
While the cookies are cooling, melt the chopped semisweet chocolate in a microwave-safe bowl in 20-second intervals, stirring between each, until smooth.
Drizzle the melted chocolate over the cooled shortbread cookies or dip half of each cookie into the chocolate. Place the cookies on parchment paper and allow the chocolate to set before serving.