Preheat oven to 350°F (175°C).
Lightly grease an 8x8-inch square baking pan with nonstick spray. Line with parchment paper; set aside.
Combine melted butter, oil, and sugar together in a medium-sized bowl. Whisk well for about a minute. Add the eggs and vanilla; beat until lighter in color (another minute).
Sift in flour, cocoa powder and salt. Gently fold the dry ingredients into the wet ingredients, along with the chocolate chips and walnuts until JUST combined (do NOT over beat as doing so well affect the texture of your brownies).
Pour batter into prepared pan, smoothing the top out evenly.
Bake for about 20 minutes, or until the center of the brownies are set and no longer jiggle (the brownies will keep baking in the hot pan out of the oven). If testing with a toothpick, the toothpick should come out dirty for fudge-textured brownies.
Remove and allow to cool to room temperature before cutting into portions and serving.