Combine and heat. In a 2-quart saucepan, mix the sugar, salt, half and half, and corn syrup. Whisk until smooth, then place over medium-low heat and bring the mixture to a gentle boil.
Cook to 240°F. Attach a candy thermometer to the side of the saucepan. Allow the mixture to cook undisturbed (do not stir) until it reaches 240°F. Immediately remove the saucepan from the heat.
Add butter and peanut butter – do not stir. Let the mixture sit until it stops bubbling. Add 2 tablespoons of butter, the peanut butter, and the vanilla extract on top. Do not stir; let it cool at room temperature for 20 minutes until the pan is warm but not hot to the touch.
Beat the fudge. Use a hand mixer at medium to low speed to beat the mixture for 1-3 minutes until it thickens and becomes smooth. Add 2 cups of powdered sugar and beat in. It will appear crumbly: this is normal!
Press, cool, and cut. Press the fudge into the buttered dish, smoothing it out as needed. Let it set for about 20 minutes at room temperature. Once set, cut into one-inch squares and enjoy! It will be softer than most stovetop fudge because of the peanut butter, but it will still cut into nice squares.