In a large bowl, using an electric/stand mixer (or hand whisk, just double/triple the times) combine the butter and both sugars on medium speed for several minutes, until fully combined. Add the egg and vanilla and mix again.
Split the dough into two bowls - either eyeball it, and do it roughly. Or you can place a bowl on scales, and weigh about 200g mixture into each bowl.
To one bowl, add the flour and baking powder. To the other, add the flour, baking powder and cocoa powder. To both, add about 100g chopped white chocolate. Stir together until a fairly stiff cookie dough forms. Chill for 30 mins in the fridge.
Preheat oven to 200C/180C Fan/Gas Mark 6. Line 2-3 large baking trays.
Scoop about a tsp of dough from each bowl and push together, to form a ball - half vanilla and half chocolate. Place on a baking tray. Repeat for all dough, placing only 3-4 balls per tray.
Bake for 9-11 minutes, until just golden at the edges. They may look underbaked in the centre but they keep cooking from the residual heat, and this gives them their perfect soft texture. Let cool on a wire rack before serving (although they are wonderful while still warm).