In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, brown sugar, and granulated sugar until light and fluffy. Add the vanilla, then the eggs, one at a time, and mix well. Sift together the flour, baking soda, and salt and, with the mixer on low speed, slowly add to the butter mixture, mixing only until combined. Fold in the walnuts and chocolate chunks.
Drop the dough on a baking sheet lined with parchment paper, using a 1 3/4-inch-diameter ice cream scoop or a rounded tablespoon. Dampen your hands and flatten the dough slightly. Bake for exactly 15 minutes (the cookies will seem underdone). Remove from the oven, sprinkle with flaked sea salt, and allow to cool slightly on the pan, then transfer to a wire rack to cool completely.