Chop the pistachios and dark chocolate; set aside. Line two baking sheets with parchment.
Brown the butter: Melt the butter in a light-colored saucepan over medium heat, stirring, until the milk solids turn deep golden and smell nutty, 3–5 minutes. Scrape into a shallow bowl to cool. Stir in the orange zest, then refrigerate 10–12 minutes until slightly opaque but still soft.
Whisk the dry ingredients in a separate bowl: flour, baking soda, baking powder, and kosher salt.
In a large mixing bowl, beat the cooled browned butter with the brown and granulated sugars using a hand mixer (or stand mixer fitted with the paddle) on medium until thick and glossy, about 1 minute. Beat in the egg and vanilla bean paste until the mixture lightens slightly, 30–45 seconds.
Add the dry ingredients and mix on low just until a few flour streaks remain. Fold in the pistachios and chocolate chunks until evenly distributed.
Cover and chill the dough for 25–30 minutes to firm slightly. While it chills, adjust the oven rack to the center position and preheat to 360°F (182°C).
Scoop 2-tablespoon portions (about 40 g) and arrange 2 inches apart on the prepared sheets. Press a few extra chocolate bits on top of each mound for a bakery look.
Bake one sheet at a time for 10–12 minutes, until edges are set and lightly golden while centers look soft. Rap the pan once on the counter right after removing to settle the cookies and encourage crinkly edges.
Immediately sprinkle with flaky sea salt. Cool on the sheet for 5 minutes, then transfer to a rack. Repeat with remaining dough and enjoy slightly warm.