Preheat the oven to 175°C.
Trim the dark brown outer crust from the panettone (optional). Cut the rest of the loaf in 1-inch cubes and place on a sheet pan in a single layer. Toast the panettone for 10 minutes, until lightly browned.
Grease a 9 by 12 by 2-inch baking dish with the butter. Place the panettone cubes in the baking dish.
In a large bowl, whisk together the whole eggs, egg yolks, half-and-half, vanilla and almond extracts and sugar. Pour this custard mixture over the panettone. Set aside for 10 minutes so the bread soaks up the custard. Scatter the sliced almonds over the top of the pudding.
Place the baking dish into a larger pan and add very hot tap water to the larger pan until it's halfway up the side of the baking dish. Cover the larger pan 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 the pudding for 45 minutes. Uncover and bake for 40 to 45 more minutes, until the custard is set and the top of the pudding is light golden brown. Allow to cool for 15 minutes. Serve warm or at room temperature.