Make chocolate syrup:
In a 1 quart casserole with lid, combine 1@ cup sugar, 1 Tablespoon baking cocoa, 2 1/2 teaspoons cornstarch, and 1/2 cup water. Cover and microwave on high 2 minutes, stir, microwave 2 more minutes, stir in 2 Tablespoons unsalted butter and 1/2 teaspoon pure vanilla extract. Use 1/4 cup of this for the milkshake and save the rest for hot fudge sundaes.
Put 1/2 cup milk, 1/4 cup of the above chocolate syrup, and blend a few seconds on high speed. Add 1 1/2 cups softened frozen vanilla yogurt and blend until smooth starting on stir and gradually increasing speed.
