Center a rack in the oven and heat the oven to 350°F.
Butter the bottom and sides of a 9x13-inch baking pan, line it with parchment (the paper should extend at least an inch above the long sides to act as handles for getting the brownies out), and butter the paper.
Put about 2 inches of water in a small pot and heat to a gentle simmer.
In a heatproof bowl set over the water, melt 8 ounces of the butter and 8 ounces of the unsweetened chocolate.
Be sure that the water is hot but not boiling and that it doesn’t touch the bottom of the bowl.
Stir occasionally with a heatproof spatula until the mixture is completely melted and uniform, 6 to 7 minutes.
Turn off the heat, but leave the bowl over the water.
In a food processor, finely grind the peppermint leaves with the sugar.
In a medium bowl, whisk together the eggs, peppermint extract, salt, and peppermint sugar until just combined.
Whisk in the melted chocolate mixture (reserve the pot of water for later).
Slowly add the flour, gently folding it in with a spatula, until incorporated.
Spread the batter into the prepared pan and bake until a pick inserted into the center comes out almost clean (a few bits of batter should cling to the pick), 35 to 40 minutes.
Put the pan on a rack to cool to room temperature, about 2 hours.
Lift the paper lining to pull the brownies out of the pan.
Peel the paper off the brownies and put them on a cutting board.
To make the glaze, bring the pot of water back to a gentle simmer.
Set a heatproof bowl over the pot and add the semisweet chocolate, corn syrup, and the remaining 2 ounces each butter and unsweetened chocolate.
Stir frequently with a heatproof spatula until the mixture is melted and smooth; set aside.
Put the white chocolate in a separate heatproof bowl and set it over the water.
Stir frequently until it’s melted and smooth; remove it from the heat.
Spread the chocolate glaze over the cooled brownies in an even layer using a spatula.
Drizzle the white chocolate over the glaze in lines.
Use a toothpick or a wooden skewer to drag the white chocolate into the glaze (as shown in the photo at left).
Lift the cutting board and firmly tap it on the counter to settle the glaze.
Refrigerate until the glaze is set, at least 20 minutes and up to 12 hours.
Cut into thirty bars, about 2 inches square (a knife rinsed in hot water and then dried will cut more cleanly than a cold knife).
Keep well covered and serve at room temperature.
These brownies only get better after a couple of days, as their texture gets fudgier and their flavor richer.