Prepare Pan: Line an 8x8 inch pan with parchment paper so it sticks out over at least 2 of the edges. Set aside.
Melt Butter and Sugar: In a large pot over medium heat, melt the vegan butter. Then, whisk in the brown sugar and salt until well combined.
Add Oats: Turn the heat to low and add in the vanilla extract, quick oats, and chopped walnuts. Mix until evenly combined. Turn off the heat and set aside.
Form Oat Crust: Press half of the oat mix (about a heaping 1 ½ cups) into the bottom of the 8x8 inch pan using a spatula or your fingers until you have firm, even layer.
Melt Chocolate: In a microwave-safe bowl, melt the chocolate chips and peanut butter in the microwave in 30-second increments until the mixture is uniform.
Layer Bars: Pour the fudge mix over the oat layer and smooth into an even layer and then sprinkle the remaining oat mix evenly over the top, gently pressing it down a little.
Chill Bars: Cover and refrigerate for at least an hour before lifting out of the pan and cutting in 16 bars. Serve right away or store in the fridge or freezer.