Tear the ciabatta into chunks and place them in the bottom of the baking dish. Sprinkle with the Cheddar, then tear the cream cheese into small pieces and place over the top. Cut the 1 1/2 sticks of butter into pats and place over the top.
Mix together the milk, onions, chives, mustard, salt, cayenne and eggs in a large bowl and pour over the top of the dish. Make sure to pour slowly, getting it all around the edges and in the crevices. Cover with foil and refrigerate overnight.
The next morning, preheat the oven to 325 degrees F.
Bake the omelet, covered, for 45 minutes. Raise the oven temperature to 350 degrees F, remove the foil and continue baking until firm and set, 10 to 15 minutes.