Preheat the oven to 350 degrees F. Space two racks evenly in the oven.
Cut five 3/4-inch-thick slices of brioche and place them in one layer on a sheet pan. Trim some of the crusts from the remaining brioche and cut in 1-inch dice. Spread out on a second sheet pan. Put both pans in the oven for 5 minutes, to lightly toast the bread.
Meanwhile, for the custard, whisk together the whole eggs, yolks, half-and-half, milk, granulated sugar, vanilla, and vanilla seeds in a large bowl, and set aside. Line a 10-by-12-by-2-inch rectangular baking dish with the whole slices of brioche, cutting them to fit in one layer. Distribute the diced brioche on top. Pour on the custard and press lightly so all the bread is soaked with custard. Set aside for 10 minutes.
Place the dish in a roasting pan large enough to allow the baking dish to sit flat. Pour about 1 inch of the hottest tap water into the roasting pan, being sure not to get any water into the custard. Cover the roasting pan tightly with aluminum foil, tenting the foil so it doesn't touch the pudding. Cut a few holes in the foil to allow steam to escape. Bake for 45 minutes. Uncover and bake for 45 to 50 minutes, until the custard is set and a knife inserted in the middle comes out clean. Dust with confectioners' sugar and serve warm, drizzled with melted ice cream.