Lightly butter a 13 by 9 by 2-inch baking dish and arrange the bread cubes in the prepared dish.
In a large bowl, whisk the eggs, cream, milk, sugar, and vanilla to blend. Pour the custard over the bread cubes, and press the bread cubes gently to submerge.
Let stand for 30 minutes, occasionally pressing the bread cubes into the custard mixture. (Recipe can be prepared up to this point 2 hours ahead. Cover and refrigerate.)
Preheat the oven to 350 degrees.
Bake until the pudding puffs and is set in the center, about 45 minutes. Cool slightly. Spoon the bread pudding into bowls and serve.