Roughly chop the basil then add to a small saucepan with the butter. Heat continuously it on medium-low on the stove until it foams up and smells nutty then stir in the vanilla extract. Leave to cool for 10 minutes, then strain it through a sieve (push through as much of the browned butter bits as poss though, you're just trying to take out the herbs).
4 tbsp fresh basil leaves, 140 g (5 oz / 1 stick + 2 tbsp) unsalted butter, 1 tbsp vanilla extract
Meanwhile, either in a stand mixer or a large bowl combine the next 6 ingredients (flour through to salt). Pour in the butter and mix until it looks like moist clumpy sand with no floury patches. Add the egg and mix in for a few seconds.
230 g (1 3/4 cups) plain white (all purpose) flour, 3/4 tsp baking powder, 3/4 tsp bicarbonate of soda, 100 g (scant 1/2 cup) granulated sugar, 140 g (1/2 cup + 1 tbsp), light brown sugar, 1/2 tsp flaky salt / fleur de sel*, 1 UK medium egg
Let the dough cool a bit (so the chocolate doesn't melt) then add the chopped chocolate and mix until well distributed - but not for too long!
200 g (7 oz) bittersweet chocolate, roughly chopped
Using a 1/4 cup cookie scoop (see notes), scoop up some of the dough and smoosh it into the scoop until it's just full. Turn out onto a lined cookie tray, and repeat with the rest of the dough. You can cram them together onto the tray at this point since we're going to chill them. Cover with cling film and refrigerate for anywhere between 1 - 72 hours (the longer you wait, the better the texture and flavour!!!).
When ready to bake preheat your oven to 400°F (200°C).
Take 4 to 6 mounds of cookie dough and place onto a separate lined baking sheet, spacing them about 7cm (3 inches) apart as they spread during baking. Sprinkle these mounds with fleur de sel and shove into the oven immediately!!
1/2 tsp flaky salt / fleur de sel*
Bake for 8-12 minutes, until browned, with set edges, and a puffy, soft center. Let cool on the baking tray for a few minutes before transferring to a wire rack.