In a saucepan, whisk together the heavy cream, milk, sugar, and salt.
Heat the mixture on low-medium heat, stirring constantly, until it barely starts to bubble and the sugar is all the way dissolved. Turn off the heat.
In a separate bowl, whisk the 4 egg yolks, and then spoon in about ⅓ of the mixture from the stove.
Whisk it all together, then pour the mixture into the saucepan, and then turn the heat back on to low-medium.
Stir the mixture a few times per minute until it starts to lightly boil. Let it lightly boil for 2 minutes, stirring constantly. If it starts becoming a rolling boil, turn off the heat and keep stirring. The temperature of the custard should be between 180F (82C) and 185F (85C), and it should be getting thick, but pourable.
Turn off the heat, and stir in the peanut butter and vanilla until everything is very well incorporated. If your peanut butter isn't mixing well, you may need to use an immersion blender or a hand mixer to get it smooth.
Strain the custard through a fine mesh strainer into a bowl. Cover the bowl with a towel and let it sit at room temperature for about an hour. Then, cover the bowl with either a lid or plastic wrap, and place it in the refrigerator for about 3 hours, or until it's set.