Grease an 8-inch square pan. Preheat oven to 350 degrees F.
Beat sugar and eggs: Using a stand mixer fitted with a paddle attachment, beat together the eggs, dark brown sugar, and vanilla on medium speed for at least 3 minutes or until the sugar is no longer gritty and the mixture has a nice sheen.
Mix the dry ingredients then combine with the wet: In a medium bowl, whisk together the flour, baking soda, and salt. Add the flour mixture to the brown sugar mixture and beat until the flour is incorporated and streak free. Stir in the walnuts.
Bake and cut into squares: Pour the batter into the prepared baking dish and smooth the top with a spatula. Bake for 18-20 minutes at 350 degrees, until the edges pull away from the sides and appear lightly brown (Cookies should be soft in center when taken from oven).
Allow the dish to cool then cut into squares. Store in an airtight container at room temperature for up to 5 days.