In a mixer, fitted with a paddle attachment, mix together white sugar, brown sugar, and corn syrup. With mixer on low, slowly stream in melted butter and mix until smooth.
With mixer on low, add milk, vanilla, and egg yolk. Mix for 30 seconds, or until combined.
Add baking soda, salt, and flour. Mix on low speed until just combined, about 45 seconds
Fold in chopped chocolate and walnuts. Mix briefly to distribute evenly for about 20-25 seconds
Scoop dough into 45g (about 2T) portions, roll lightly, and place on a parchment-lined baking sheet. Press a piece of chocolate on top of each cookie. Refridgerate for 10 minutes.
Sprinkle with flaky salt and bake for 14-16 minutes at 325°F (165°C), until cookies are golden and crisp.
Let the cookies fully cool before serving.