Preheat the oven and prepare the pan: Preheat the oven to 350 °F (175 °C) and grease a 10×15 inch jelly-roll pan or a 9×13 inch baking pan.

Mix melted butter, oil and cocoa: In a large bowl, whisk together the melted butter, vegetable oil, and unsweetened cocoa powder until smooth.

Add dry ingredients: Stir in the salt, flour, granulated sugar, and dark brown sugar until the mixture begins to hold together.

Incorporate eggs and vanilla: Whisk in the eggs and vanilla extract until the batter is evenly combined and glossy.

Spread the batter: Pour the batter into the prepared pan and spread it evenly using a spatula or the back of a spoon.

Bake the brownies: For the 10×15 pan, bake for about 15–20 minutes. For a 9×13 pan, bake 25–30 minutes. The brownies are done when the surface is matte and bubbly, and the center is bouncy to the touch.

Prepare the frosting right away: Just as the brownies come out of the oven, begin the frosting. In a bowl using a hand mixer or stand mixer with the paddle attachment, mix together the softened butter, pinch of salt, and cocoa powder. Then add the powdered sugar one cup at a time, followed by the milk and vanilla extract, mixing until smooth.

Frost the warm brownies and add sprinkles: Spread the frosting evenly on the warm brownies, then immediately top with rainbow sprinkles for that vibrant finish.

Cool completely and slice: Allow the brownies to cool completely in the pan before slicing into squares for clean edges and the perfect texture.