Preheat oven to 350° F. Grease and parchment line an 8-inch square baking dish, set aside.
In a medium-sized bowl, whisk together butter, avocado oil, and sugar. Whisk well for 1-2 minutes. Add the eggs and vanilla, whisk for an additional 2 minutes, until light in color.
In a small bowl, whisk together the flour, cocoa powder, and salt. Carefully fold the dry ingredients into the egg butter mixture, until just combined.
Pour the batter into the prepared pan, spread out evenly. Sprinkle the top with the chopped walnuts. Bake for 20-25 minutes, or until just set. (Brownies will be soft and chocolaty with a crackled top.) Allow the brownies to cool before frosting.
Make frosting according to recipe instructions. Pour all of the frosting over the cooled brownies. Using a spatula, evenly spread out the frosting over the brownies. Swirl frosting with the back of a spoon for a decorative effect. Allow brownies to chill before slicing into squares.
Store in an air-tight container in the refrigerator for up to 5 days.