Heat the butter in a saucepan over medium heat, gently moving it around the pan as it melts and browns. Look for golden-brown milk solids beneath the foam and a toasted, nutty aroma.
Transfer the butter and browned flecks to a heatproof measuring glass, whisk in the miso, and leave the mixture to cool. The paste should disperse without visible clumps, and the butter should be fluid but no longer hot before mixing the dough.
Set the oven to 350°F and cover a large baking sheet with parchment paper. Keep the parchment flat so the dough portions sit evenly on the sheet.
Blend the flour, baking powder, baking soda, and salt with a whisk in a medium bowl. The mixture should look uniform, with no obvious pockets of leavener.
Whisk both sugars with the cooled butter-miso mixture in a large bowl. Scrape through any brown sugar lumps until the mixture looks evenly combined.
Beat the egg and vanilla into the sugar mixture with a vigorous whisking motion. Continue until it becomes paler, creamy, and thick enough to briefly trail from the whisk.
Fold the flour mixture into the wet mixture with a rubber spatula, adding the chopped chocolate while some flour remains visible. Stop folding once the flour disappears and the chocolate distributes throughout the dough.
Portion the dough with a large 2 oz scoop or a 1/4 cup measuring cup. Keep the portions similar in size so they bake at the same pace.
Pour the sesame seeds into a shallow dish and dip the upper surface of each dough portion into them. The seeds should coat the tops without covering the entire dough ball.
Arrange four portions on the prepared sheet with a few inches between them, then bake for 11–13 minutes. Remove them when the edges look light golden and the centers remain soft, slightly puffy, and barely underdone.
Leave the cookies on the baking sheet for about 5 minutes before moving them to a cooling rack, then bake the remaining portions. The edges should firm enough to lift while the centers continue setting from the pan’s residual heat.
Allow about 20–30 minutes of cooling before serving. The centers will settle into a chewy texture while the chocolate pockets remain soft.