Preheat your oven to 350°F (175°C). Spread the chopped walnuts evenly on a baking sheet and toast them in the oven for about 8-10 minutes, or until they are golden and fragrant.

In a large mixing bowl, combine the softened unsalted butter, brown sugar, and granulated sugar. Use an electric mixer to beat the mixture on medium speed for 2-3 minutes, or until it becomes light and fluffy.

With the mixer on low speed, add in the whole egg, egg yolk, and vanilla extract to the sugar-butter mixture. Mix until everything is well combined.

In a separate bowl, whisk together the all-purpose flour, cornstarch, baking soda, and salt. Gradually add the dry mixture to the wet ingredients, stirring gently until a soft dough forms.

Gently fold in the semi-sweet chocolate chips and the toasted walnuts until evenly distributed.

Use a cookie scoop to portion the dough onto a parchment-lined baking sheet. Cover with plastic wrap and chill in the refrigerator for at least 30 minutes.

Preheat your oven again to 350°F (175°C) if it has cooled down. Bake for 11-13 minutes until the edges are golden and the centers are slightly underbaked.

Let the cookies rest on the hot baking sheet for about 5 minutes before transferring to a wire rack to cool completely.