Lightly grease and line a 6x 6-inch pan with parchment paper, leaving a 2-inch overhang for easy unmolding. Set aside.
In a large heavy-bottomed saucepan stir together both sugars, half-and-half, butter, and salt over medium-low heat. Stir until the sugar is completely dissolved. Increase the temperature to medium and cook the mixture, stirring occasionally, until it comes to a boil. Clip a candy thermometer onto the side of the pot and boil the sugar mixture until it reaches the softball stage or 240°F on the candy thermometer. Do not stir the mixture at this point. Remove pot from the heat immediately then add vanilla, do not stir. Gently place the pan on top of a cooling rack. Leave the candy thermometer inserted in the mixture and allow cooling to 130°F.
Beat with a hand held mixer for 2 minutes on low speed until it lightens in color, thickens, and begins to lose its shine but is still pourable. Do not over beat.
Quickly add walnuts and pour the mixture into the prepared pan. Sprinkle some walnuts over the top, pressing them into the fudge to level the fudge in the pan. Cool completely before cutting.
Make sure the sugar is completely dissolved before the mixture begins to boil, if not, the result will be a granular fudge.
Be gentle when removing the saucepan from the heat. Make sure you do not stir the fudge until it achieves 130°F.
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