In a medium pan over medium heat, melt 10 ½ tablespoons (150g) butter, stirring frequently.
Increase heat to medium-high, swirling the pan often. The butter will start to turn amber and smell nutty. Continue to cook butter until it darkens a bit more. (Butter will momentarily foam as it cooks.)
Pour burnt butter into a heatproof bowl and place in fridge. Leave butter in fridge until it firms up some but is still soft (similar to room temperature butter). Make sure to stir the butter every so often.
Once burnt butter is the proper consistency, remove from fridge and combine with remaining plain butter. Re-measure/re-weigh and add as much additional plain butter as necessary to reach 1 cup (226g) total. NOTE: We had to add 30g (roughly 2 tablespoons).
In the bowl of a stand mixer fitted with paddle attachment, beat butter and sugars on medium-high until light and fluffy.
Add egg and vanilla, mixing until thoroughly combined. At this point, the mixture should be light in colour and aerated.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt. Add half of the flour mixture to butter mixture, mixing until it’s almost all incorporated. Scrape down bowl. Repeat once more with rest of flour mixture.
Mix in chocolate chunks and walnuts pieces.
Using a wooden spoon, fold halva chunks into cookie dough.
Cover bowl with a beeswax wrap or clean dish towel and refrigerate for 30 minutes.
While dough is chilling, heat oven to 350°F. Line baking sheets with parchment paper.
Form dough into balls that are 1.5–2 tablespoons each. (A cookie scoop is super helpful here.) Place 8 dough balls on each prepared baking sheet, leaving plenty of space between them. Sprinkle flaky salt on top.
Bake for 8 minutes, then open oven door and with an oven-mitted hand, raise baking sheet a few inches and—with a little force—tap sheet against oven rack. You’ll see the cookie deflate a smidge and the chocolate begin to spread.
Close oven door and bake for 2 minutes more. Repeat raise and tap process.
Close oven door and bake for 2 additional minutes. NOTE: This raising and tapping business causes the cookies to spread and will give you lovely pools of chocolate. If you don’t really care about that and/or can’t be arsed, simply bake cookies for 10–12 minutes until edges are set.
Remove from oven and cool on baking sheets for 5 minutes. Transfer cookies to a wire rack to cool completely.
Since some of the butter will evaporate when it is browned, you will need to add a little extra during the re-measure/re-weigh. (For example, we had to add 30g more.)