In a mixing bowl, sift the flour and white sugar together and stir in 1 egg and the vanilla essence until well combined. Using a pastry cutter, cut the cold butter into the mixture until it resembles coarse meal. Shape the dough into a ball, wrap it in plastic wrap and refrigerate for 20 minutes.
Divide the dough in half and roll into two 30cm logs. Wrap one of the logs in baking paper and then cling wrap and refrigerate overnight. Place 3 tablespoons of coarse sugar crystals on a flat plate. Brush the second log with beaten egg and roll it in the sugar crystals, coating it thickly. Carefully wrap the sugared log in cling wrap and refrigerate overnight.
Preheat the oven to 200 degrees C and line baking trays with baking paper.
Cut the unsugared log of dough into round slices about 3mm thick and place the rounds onto the prepared baking trays, about 1cm apart. Top each with a pecan half. Cut the sugared log of dough into 3mm thick slices and place them onto prepared baking trays. Sprinkle each sugared cookie with more coarse sugar crystals, if desired.
Place one baking tray of biscuits at a time into the preheated oven and bake until the edges barely turn golden, 4 to 5 minutes. Remove the biscuits to wire racks to cool.