Make the toffee first. Line a small baking sheet or plate with parchment paper. Add the 115 grams unsalted butter, 135 grams caster sugar, 2 tablespoon water and ½ teaspoon fine sea salt to a small saucepan over a medium heat.
Cook the toffee. Stir as the butter melts, then keep cooking, stirring frequently, until the mixture turns a deep golden amber and reaches around 149°C (300°F).
Finish the toffee. Take the pan off the heat and carefully stir in the 1 teaspoon vanilla extract.
Set the toffee. Pour the toffee onto the prepared parchment and spread it into a thin layer. Sprinkle lightly with Flaky sea salt and leave it to cool completely until it's hard.
Chop the toffee. Break or chop the cooled toffee into small pieces, about 0.5 to 1cm. Set aside 1 cup of it for the cookie dough.
Brown the butter. Add the 340 grams unsalted butter to a light-coloured saucepan over a medium heat. Let it melt, then keep cooking, stirring or swirling frequently. It will foam up as it cooks, so keep going until the milk solids turn golden brown and it smells deeply nutty and toasted. Pour it straight into a large heatproof mixing bowl, scraping in all those browned bits.
Cool the butter. Leave the brown butter to cool for 15 to 20 minutes, until it's warm but no longer hot.
Mix the dry ingredients. In a separate bowl, whisk together the 440 grams plain flour, 1 ½ teaspoon bicarbonate of soda and 1 teaspoon fine sea salt.
Combine the butter and sugars. Add the 300 grams packed dark brown sugar and 100 grams caster sugar to the cooled brown butter and whisk until smooth and well combined.
Add the eggs. Whisk in the 2 large eggs, 2 large egg yolks and 4 teaspoons vanilla extract until the mixture is smooth and slightly thickened.
Add the dry ingredients. Fold the flour mixture into the wet ingredients with a spatula, mixing just until the flour is almost completely incorporated. Take care not to overmix.
Add the chocolate and toffee. Fold in the 200 grams milk chocolate chunks 150 grams milk chocolate chips and 1 cup homemade salted toffee pieces, saving a little of each back for topping the cookies after baking.
Chill the dough. Cover the bowl and refrigerate for at least 1 hour. For the best flavour and texture, chill for 2 hours or even overnight.
Get ready to bake. Preheat your oven to 175°C (350°F) and line baking sheets with parchment paper. Scoop the dough into around 24 portions, roughly 65 to 70g each, and place them several inches apart on the prepared trays.
Bake. Bake for 10 to 12 minutes, until the edges are golden brown and set but the centres still look soft and slightly underbaked.
Finish while warm. As soon as the cookies come out of the oven, press a few extra chocolate chunks and toffee pieces into the tops and sprinkle with Flaky sea salt.
Cool. Leave the cookies to cool on the baking sheet for 10 minutes before transferring them to a wire rack.