2 tablespoons unsalted butter, cut into small pieces and softened, plus more for brushing
3 ounces unsweetened chocolate, very finely chopped
1 teaspoon vanilla, mint or almond extract
1/8 teaspoon kosher salt
1 cup half-and-half
2 1/4 cups sugar
2 tablespoons light corn syrup
Assorted toppings (see below)