Combine all ingredients except butter and vanilla. Combine all ingredients except butter and vanilla. In a 2 quart saucepan, combine the sugar, half and half, salt, and corn syrup. Mix well with a whisk and bring to a boil over medium-low heat. While the fudge is cooking, butter a plate or baking dish for pouring the mixture into later.
Heat until the mixture reaches 240 degrees. Let the fudge cook until it reaches 240 degrees, checked with a candy thermometer or instant-read thermometer. Don't stir during the cooking process. Once the temperature is reached, immediately remove the pan from the heat.
Place butter and vanilla on top and allow to cool. Give the sugar mixture a minute to stop bubbling, then place the butter and vanilla on top and allow to cool at room temperature. Do not mix now or otherwise disturb the pan. Let it cool for about 20 minutes until the side of the pan is warm, but not hot to the touch.
Mix with a hand mixer until fudge begins to firm up. Using a hand mixer on medium-low, beat the fudge for 1-3 minutes until it just begins to firm up and lose its shine. Do not overbeat, or the fudge will be too hard to pour.
Quickly pour into a buttered dish, cool, and cut. Quickly pour into a buttered dish, cool, and cut. Once the fudge changes texture, immediately pour it into a dish to set. Work quickly. It if is not pourable, just scoop it out and flatten in the best you can. Allow it to cool for 20 minutes and cut into one-inch squares.