Preheat the oven and prepare an 8x12-inch baking pan by greasing it and lining it with parchment paper, leaving an overhang on the sides for easy removal.
In a large mixing bowl, whisk together the melted butter, vegetable oil, white sugar, and brown sugar until the mixture is well combined and glossy.
Add the room-temperature eggs and vanilla extract to the sugar mixture, whisking vigorously for at least one full minute until the batter becomes slightly lighter in color.
Sift the all-purpose flour, cocoa powder, and salt directly into the wet ingredients to ensure there are no lumps in the batter.
Use a spatula to gently fold the dry ingredients into the wet mixture, stopping the moment you no longer see any white streaks of flour.
Fold in about three-quarters of the chopped chocolate pieces, then pour the thick batter into the prepared pan and smooth the top.
Sprinkle the remaining chocolate pieces over the surface and bake until the edges are firm but the center still has a very slight jiggle.
Remove from the oven and allow the brownies to cool completely in the pan for at least 20 minutes before lifting them out and slicing into squares.