Add one stick of butter to a medium skillet over medium heat. Allow it to melt and bubble up for 3 to 4 minutes, swirling the pan to keep the butter moving around. When the butter is a medium golden brown, remove the pan from the heat (it will continue browning in the pan over the next 30 seconds or so!) Pour butter (and any solids in the bottom of the pan) into a heatproof bowl and allow it to cool completely, about 30 minutes. Meanwhile, allow the other stick of butter to soften. Preheat the oven to 375°F. Cream the softened butter together with the brown sugar and regular sugar until it's nice and combined. Add the eggs and vanilla, and beat until smooth, scraping the bowl if necessary to make sure everything is incorporated. With the mixer on medium-low, very slowly drizzle in the cooled melted butter, making sure to add all the darker brown solids. Scrape the bowl the mix again for 20-30 seconds, until everything is combined. In a separate bowl, combine the flour, coffee granules, baking soda and salt. Stir together, then add it in 1/3 increments, mixing on low, until it's totally incorporated. Scrape the bowl and beat for a few more seconds. Stir in the chocolate chunks and nuts, if using. In batches, scoop by heaping teaspoon onto a baking sheet lined with a baking mat, Press extra chocolate chunks into the tops of each cookie, if desired. Refrigerate scoped cookies for 15 minutes, then bake for 9 to 10 minutes, or until golden brown. Remove from oven, then transfer cookies to a cooling rack. Repeat with the rest of the dough.
Serve with cold milk.