Make sure the butter is completely at room temperature. Add it to a large bowl and beat it a little with a wooden spoon just to soften it up further. You can make shortbread dough in a stand mixer if you want, but use it on the lowest speed and be very careful not to overmix it.
Add the sugar and mix it just until incorporated - don't cream it until light and fluffy like you would with a cake. Just combine until smooth.
Add the flour and mix until it starts forming a shaggy dough. Do not overmix, just until it comes together. Ditch the spoon and use your hands to bring it together into a smooth dough.
Add the chocolate and knead through gently.
For Cutout Cookies
Roll the dough out on a floured surface to between ¼ inch and ½ inch thickness. Cut into desired shapes with a cookie cutter and place onto a baking sheet lined with parchment paper.If it's too soft to roll out, put it in the fridge for 10 minutes to firm up.
Sprinkle the shortbread cookies generously with sugar and put them in the fridge to chill for 1 hour. Preheat the oven to 325°F / 160°C (140° fan-assisted).
For Slice-and-Bake Cookies
Divide the shortbread dough in half and shape into two logs, about 2 inches in diameter. Wrap the logs in plastic wrap and roll them gently on the counter to smooth out the edges. Chill the dough logs in the fridge for an hour to firm up, then preheat the oven to 325°F / 160°C (140° fan-assisted).
Once the dough is firm, unwrap from the plastic wrap and use a sharp knife to cut ¼ inch to ½ inch rounds. Place them on a baking sheet lined with parchment paper with a little room to spread, and sprinkle generously with sugar.
Bake
Bake for 20-25 minutes, or until the very edges of the cookies are starting to turn golden brown. They should still look very pale when baked.
Remove from the oven and let them sit on the baking sheet for 10 minutes before transferring to a wire rack to cool.
Notes
The number of cookies made from this dough will vary depending on the size and thickness of your cookies. For the slice-and-bake method, it may be better to use smaller chocolate chips as large ones can make it difficult to get clean slices.