Heat oven to 350 F and butter a 9"x13" baking dish.
In a bowl, whisk the cocoa powder with 1/2 cup plus 2 tablespoons boiling water.
Melt the chocolate and butter in a double boiler, or in a metal bowl set over a saucepan of simmering water.
Whisk in the cocoa mixture.
In a large bowl, whisk together the sugar, oil, eggs, egg yolks, and vanilla.
Whisk in the chocolate mixture. Sift the flour and salt into the batter, and stir to combine.
Stir in 2 cups of the toffee chips and the chocolate chips (1 cup).
Use a rubber spatula to transfer the batter to the prepared baking dish.
Bake until a tester inserted in the middle of the pan comes out clean, about 40 minutes.
Allow the brownies to cool completely on a wire rack before icing.