My mom used to make this every Christmas when I was a kid, it was one of my favorites, I figured it was not able to be veganized, so I never looked... until today!
1) Oil desired size pan (I like mine thick, so I use an 8" pan). Mix together nondairy milk and sugar in heavy-bottomed medium sized saucepan over medium heat. Boil until it reaches soft ball stage (a drop rolls into a soft ball in cold water) or 234 degrees Fahrenheit. Remove from heat and quickly stir in vanilla and peanut butter. Immediately pour into prepared pan. Let cool completely. When cooled, it should be crumbly and hard to cut without cracking. But it will melt in your mouth.
*To make peanut milk, put a cup of peanuts in food processor, grind until it makes peanut butter, add 3-4 cups of water. The leftovers are great in other dessert recipes.
Source of recipe: A variation of my grandmothers recipe.