Cream the butter and sugars.
In a large mixing bowl, beat the softened butter, brown sugar, and granulated sugar with a hand mixer for 2–3 minutes, until light and creamy.
Add the eggs and vanilla.
Add the eggs one at a time, mixing until incorporated. Add the vanilla and scrape down the sides of the bowl. Stop once the mixture is evenly combined.
Add the dry ingredients.
In a separate bowl, whisk together the flour, cornstarch, baking soda, and salt.
Add to the butter mixture and mix on low until about halfway combined.
Fold in the chocolate and walnuts.
Add the chocolate and chopped walnuts. Fold gently until evenly distributed and no dry flour remains. Avoid overmixing.
Shape and chill.
Portion the dough into large mounds about 2 1/2 inches across. Keep them tall and loosely shaped rather than pressing them flat.
Place on a lined tray, cover, and refrigerate for 2 hours or freeze for about 1 hour, until firm.
Prepare the oven.
Preheat the oven to 350°F. Line a baking sheet with parchment paper.
Arrange the chilled dough portions about 3 inches apart, baking in batches as needed.
Bake.
Begin checking at 13–15 minutes. The edges should be golden and the tops set, with centers that remain soft but do not look wet or raw. Large cookies may require several additional minutes, especially when baked from frozen.
Cool before serving.
Let the cookies rest on the baking sheet for at least 10 minutes before transferring to a wire rack. They will be delicate when hot and will continue to firm as they cool.
Serve warm for melted chocolate and a soft center.