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 12 minutes (if the butter isn’t browning by then, turn the heat back up to medium and whisk often). Once golden brown (with amber 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 4 ounces of chopped chocolate to the bowl. Mix on low just to combine.
Use a 2-oz cookie scoop to scoop the dough onto a cookie sheet, spacing the cookies 2-3 inches apart (the cookies will spread a good amount, so use multiple sheets to allow for enough spacing). Distribute the remaining 2 ounces of chocolate onto the tops of the cookies, pressing gently.
Bake the cookies for approximately 11 minutes on the middle rack of the oven, or until brown and crisp on the outside (the middle should look underdone). Let the cookies sit on the cookie sheets for about 8 minutes at room temperature. Use a metal spatula to carefully transfer them to a cooling rack.
Sprinkle with flaky sea salt. Eat warm or cool completely.