My maternal grandmother made this all the time. My family has been making it for well over 50 years. It’s the best I have ever had. Melts in your mouth.
Line an 8x8 or 9x9 pan with foil (bright side up) and butter the foil. You can also butter a platter as well. I find the foil lined pan easiest.
Place sugar, milk, butter and salt in a heavy saucepan. Bring ingredients to a rolling boil, stirring constantly with a wooden spoon. Maintain rolling boil and stir until it reaches hard ball stage on a candy thermometer. Remove from heat.
Stir in vanilla and peanut butter. When it starts to thicken slightly, pour into your prepared pan/platter. This will thicken pretty fast so be careful.
Let cool completely. If you use the foil in the pan method (I suggest you do), just lift the foil out of the pan. Turn upside-down onto your cutting surface. Peel the foil off the fudge and turn with top side up. Cut into desired size pieces. If using a platter, just cut into pieces on the platter.