Preheat your oven to 160°C and line a baking tray with parchment paper.
In a medium saucepan, melt the butter and continue cooking until it foams and starts to brown. Remove from heat and pour into a ceramic bowl to cool.
Once the butter has cooled, add the vanilla extract, light brown sugar, and caster sugar. Whisk until well combined.
Add the eggs one at a time, whisking well after each addition.
Sift the plain flour, baking powder, and bicarbonate of soda into the butter-sugar mixture. Stir until just combined, being careful not to overmix.
Fold in the chopped white chocolate.
Using a cookie scoop or tablespoon, drop tablespoon-sized scoops of cookie dough onto the prepared baking tray. Sprinkle with sea salt if using.
Bake in the preheated oven for 10-12 minutes, or until the edges are set and the middles are still soft.
Allow the cookies to cool on the tray for about 5 minutes before transferring to a wire rack to cool completely.