3 ounces semisweet chocolate, chopped
2 tablespoons white sugar
2 teaspoons unsweetened cocoa powder
1 teaspoon vanilla extract
1 1/2 cups milk, divided
3 cups ice
Microwave chocolate in a small microwave-safe bowl, stirring every 30 seconds until melted, 5 to 7 minutes. Stir in sugar, cocoa powder, and vanilla extract until blended. Whisk in 1/2 cup milk until combined; set aside to cool, about 5 minutes.
Pour chocolate mixture, remaining milk, and ice into a blender; blend on high speed until mixture is creamy, about 1 to 3 minutes.