In a medium mixing bowl, combine the unsweetened cocoa powder and boiling water. Stir until smooth, then add the chopped unsweetened chocolate. Mix until the chocolate is completely melted and the mixture is glossy. Set this bowl aside to cool slightly.
In a large mixing bowl, whisk together the melted unsalted butter and vegetable oil until well combined. Then, whisk in the eggs, egg yolks, and vanilla extract until the mixture is smooth and slightly frothy.
Add the cocoa mixture to the wet ingredients, stirring until fully incorporated.
In another bowl, mix together the granulated sugar, flour, and salt. Gradually add this dry mixture to your chocolate batter, folding gently with a spatula until just combined.
Gently fold in the semi-sweet chocolate chunks, distributing them evenly throughout the batter.
Pour the brownie batter into your prepared 9x13-inch baking pan. Spread it out evenly with a spatula. Bake in your preheated oven for 20 to 25 minutes.
Once baked, remove the brownies from the oven and allow them to cool in the pan for about 10 minutes. Then transfer to a wire rack to cool completely before cutting into squares.