• 6 oz. milk chocolate, coarsely chopped
Arrange an oven rack in the center position and preheat the oven to 350 degrees. Line an 8-by-8-inch pan with 2 sheets of foil, crossing one over the other and pressing the foil into the corners and up the sides. Lightly butter the foil and set aside.
In a large heatproof bowl, whisk the cocoa powder and 1/4 c. boiling water until smooth (this will bring out the flavor of the cocoa).
Add the semisweet chocolate, butter and oil to the bowl with the cocoa mixture and set it over a medium saucepan filled with about 1 inch of simmering (not boiling) water (make sure the bottom of the bowl isn't touching the water). Warm the mixture gently, stirring occasionally, until the chocolate and butter are melted and the mixture is smooth. Remove the bowl from the heat and let cool until lukewarm.
Whisk the granulated and brown sugars into the chocolate mixture. It will look grainy and you might see some of the fat start to separate from the rest of the mixture, which is normal. Add the whole egg, egg yolks and vanilla and whisk vigorously until the mixture comes back together and looks very thick, smooth and glossy.