Preheat oven to 180 C / Gas 4. Line a baking tray with a silicone baking mat or parchment.
Put butter, caster sugar, brown sugar, vanilla, bicarbonate of soda and salt in a bowl. Cream together with a mixer until butter clings to sides of bowl and is uniform in colour, about 2 minutes. Mix in eggs 1 at a time, waiting until first is incorporated before adding second. Add 250g flour; mix on low speed until incorporated - the dough will be very soft.
Divide dough roughly in half and transfer one half to a separate bowl. Mix remaining flour into one half, then stir in dark chocolate chips until evenly distributed. Mix cocoa powder into other half, then stir in white chocolate chips until evenly distributed.
Roll a tablespoon of each dough into a ball and tap lightly on counter to create a flat bottom. Press flat sides together to form a larger ball, then flatten into a half-dark, half-light disk. Cut disk in half with a knife, cutting perpendicular to dough seam. Flip one half over and then firmly press halves back together. You should have a disk with 4 alternating quarters. Repeat with remaining dough. Transfer to baking sheet, spacing about 5cm apart. Sprinkle with flaky sea salt.
Bake until cookie edges start to turn golden brown, 10 to 12 minutes. Cool on tray for 10 minutes. Transfer to a wire rack to cool completely.