Preheat the oven to 350°F. Add the walnuts to a skillet and roast for 8-10 minutes, or until browned and fragrant. Allow to fully cool.
Meanwhile, add the butter to a 2 qt saucepan over medium heat. Let the butter melt. Turn the heat to medium-low and continue to cook until the butter is browned, swirling often, about 6 minutes. Once deeply golden brown (with dark brown speckles running throughout), turn off the heat and let the butter cool for a couple of minutes.
Add the brown sugar, granulated sugar, honey, and browned butter to the bowl of a stand mixer fitted with a paddle attachment. Mix on low speed to combine. Add the eggs, one at a time, mixing on medium to incorporate. Mix in the vanilla extract.
In a separate bowl, whisk the flour, salt, and baking soda together. In two batches, mix the dry ingredients into the wet. Use a rubber spatula to scrape down the sides and bottom of the bowl as needed to ensure all of the ingredients are incorporated well.
Roughly chop the cooled walnuts. Add them, along with the oats and chopped chocolate to the bowl. Mix on low just to combine.
Use a 2-oz cookie scoop to scoop the batter onto a cookie sheet, spacing the cookies about 2 inches apart (the cookies will spread a good amount, so use multiple sheets to allow for enough spacing).
Bake the cookies for 12 minutes (on the middle rack) and about 14 minutes (on the bottom rack), or until deeply golden. Cool the cookies on the sheets for 8 minutes. Carefully use a metal spatula to transfer them to a cooling rack.