Preheat oven at 180° C and butter a large baking dish.
In a large bowl, whisk together the eggs until the yolks and whites are blended. Whisk in the melted butter, brown sugar, milk, rum, and vanilla.
Add the bread cubes into the prepared baking dish and drizzle egg mixture over it.
Bake for about 30 minutes or until the top is lightly browned and the liquid is absorbed by the bread. Meanwhile, grind the poppy seeds in a food processor or coffee grinder.
Remove pudding from oven and sprinkle with poppy seeds and honey. Place back in oven for additional 10 minutes.
When pudding is done, add a dusting of confectioners’ sugar and serve hot.