All ingredients—but butter and vanilla—should be combined. Combine the sugar, half-and-half, cocoa, salt, and corn syrup in a 2-quart pot. Using a whisk, thoroughly combine and heat to a boil. Butter a plate or baking dish to subsequently pour the mixture into while the fudge is cooking.
The mixture should be heated to 240 degrees. Fudge should be cooked until a candy thermometer or instant-read thermometer registers 240 degrees. During the cooking phase, don't stir. As soon as the desired temperature is attained, turn off the heat and remove the pan.
Butter and vanilla should be added, then let cool. Allow the fudge to cool before adding the butter and vanilla. Don't stir or agitate the pan. Allow it to cool down. 20 minutes, or until the pan side is warm to the touch but not heated.
Use a hand mixer to stir until the fudge starts to thicken up. Beat the fudge for 1-3 minutes on medium-low speed with a hand mixer until it just starts to stiffen up and lose its sheen.
Pour quickly into a buttered dish, let cool, then slice. Pour the fudge into a dish to set as soon as its texture changes. Work swiftly. If it cannot be poured, simply scoop it out and flatten it as much as you can. Cut it into one-inch squares after letting it cool for 20 minutes.