Position rack in the lower third of the oven and heat oven to 325 degrees F. Use an 8 by 8-inch silicone baking pan or line a similar sized metal or glass baking dish with foil or parchment paper so it hangs over the edges by about 1 inch. For mini brownie bites, line mini muffin tins with 36 mini muffin liners. Spray the prepared pan.
Put the butter, oil and chocolate in a microwave-safe bowl, and heat at 75 percent power for 2 minutes. Stir, and microwave again until completely melted, about 2 minutes more. (Alternatively put the chocolate and butter in a heatproof bowl. Bring a saucepan filled with 1 inch or so of water to a very slow simmer; set the bowl over, not touching, the water, and stir occasionally until melted and smooth.)
Stir the brown and white sugars, vanilla and salt into the chocolate mixture with a wooden spoon. Add the eggs and beat vigorously until fully incorporated and the batter is thick and glossy. Add the cocoa, flour and baking soda and stir just until it disappears.
Pour the batter into the pan and bake until the top is crispy and a toothpick inserted into the middle comes out with a few crumbs, about 30 minutes (40 minutes if not using silicone) for pan brownies, and 14 to 15 minutes for mini brownie bites.
Cool the brownies in the pan on the counter. Lift brownies out of the pan by the foil, if needed. Peel off the foil and cut into squares, sticks or shapes using a cookie cutter. Serve. Store extra brownies in a tightly sealed container at room temperature for up to 3 days.
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