Line the bottom and sides of an 8 x 8 inch baking pan with parchment paper, leaving a bit of paper hanging over the edges of the pan. You'll use this later on to lift the fudge out of the pan.
Fill the bottom of a double boiler with water, place it over high heat and bring it to a boil, then lower the heat until it's just simmering. Place the chocolate chips and non-dairy milk into the top half of your double boiler. Cut the butter into three or four slices and add it to the pot.
Place the top half of your double boiler over the bottom. Slowly heat the ingredients up, stirring constantly.
Once the chocolate and butter have fully melted, remove the pot from heat. Begin stirring the powdered sugar into the chocolate mixture, adding a bit at a time.
Stir in the vanilla, then the walnuts.
Transfer the mixture to the prepared baking pan, pressing it in and smoothing out the top as much as you can.
Place the pan into the refrigerator and chill the fudge until it has completely set, about three hours.
Use the excess parchment paper to gently lift the entire block of fudge from the pan. Cut the fudge into squares. Serve or chill for later.