2 1/2 cups whole milk
1/2 cup granulated sugar
1/3 cup unsweetened cocoa powder (not Dutch process)
2 tablespoons cornstarch
4 ounces semisweet chocolate, chopped, plus more for garnish, optional
2 teaspoons pure vanilla extract
Kosher salt
2 tablespoons unsalted butter
1 cup whipping cream
1/4 cup confectioners' sugar