Melt butter in a small saucepan over medium heat. Continue cooking, stirring consistently, until butter foams and then turns amber and smells nutty, about 5-6 minutes. Watch carefully to prevent burning.
Let butter cool slightly, then pour into a mixing bowl with both sugars. Mix until well combined.
Add egg and vanilla to the butter-sugar mixture and mix well using a mixer or hand beater.
In a separate bowl, whisk together flour, baking soda, and salt.
Add dry ingredients to wet ingredients and mix until just combined. Don't overmix - stop once the flour is incorporated.
Fold in chocolate chips and pistachios.
Chill dough in the refrigerator for at least 1 hour, preferably 4-6 hours (or up to 24 hours for larger cookies).
Preheat oven to 350°F. Line a baking sheet with parchment paper.
Scoop dough onto prepared baking sheet, spacing cookies about 2 inches apart.
Bake small cookies for 8-10 minutes or large cookies for 11-13 minutes, until edges are golden brown but centers still look slightly soft.
Let cool on the baking sheet for 5 minutes before transferring to a wire rack.
Sprinkle with flaked sea salt while still warm. Enjoy!