Beat the powdered sugar, 1 egg and vanilla with a mixer. Sift flour and add a pinch of salt. Cut the chilled butter and chocolate into pieces (large). Mix the butter with the flour, add the egg mixture and beat everything together briefly.
Add the chocolate pieces and beat once more. The easiest way is to use a food processor. Move the dough to a kitchen counter, shape a roll, wrap it in foil and let it sit in a cold place for several hours. Remove it, sprinkle sugar on the counter and form the roll again.
Cut biscuits out, arrange them on a baking sheet and put them to bake in preheated oven for 6-7 minutes at 356°F (180 °C). You do not need to bake any longer than that because they burn easily.