Preheat the oven to 350°F / 175°C. Butter and line an 8x4" loaf pan with parchment paper.
Brown the butter: In a small saucepan set over medium heat, melt the butter. Stir the butter occasionally until it turns amber in color and develops little brown specks.
Pour the brown butter into a medium sized mixing bowl and set it in the freezer for 5 minutes.
To the brown butter, whisk in the brown sugar and granulated sugar.
Whisk in the egg yolk, milk and vanilla until very well combined.
Add in the flour, oats, baking soda, baking powder, and salt. Use a rubber spatula to fold the mixture together until only a few flour streaks remain. Add in the pistachios, and continue folding just until no flour streaks remain.
Transfer ~⅔ of the cookie dough to the prepared baking pan. Use your hands or the back of a measuring cup to pat the dough down into an even layer. Bake for 12-15 minutes, until the edges start to turn golden brown.
While the first layer is baking, make the fudge.