Does Rudolph like broccoli?

Should I ever write a children's book, I will call it "Does Rudolph Like Broccoli?" with a subhead of "And Other Random Questions from a three year old".
Christmas morning started this way for us yesterday. The boy crept into our bed at gone 3.30 and climbed down beside us. We urged him to go back to sleep as it was much too early and he snuggled down (pushing me and the husband to opposite sides of the bed).
I was just drifting off to sleep when "Does Rudolph like broccoli?" assaulted my ears. "Muuummeeee!" the boy insisted as I tried to ignore him and fake sleep. "Does he? Does Rudolph like broccoli or is it just carrots?"
"He likes all good food," I answered and shhhed him again.
"But does he like tatoes... and gravy... and turkey too?"
"Yes, yes I imagine he does..."
etc etc etc

My son has developed quite the habit of the random 3am question. It could be (as it has been lately) "When will the baby Jesus be old enough to play with me?", or "Jack in my school thinks he is getting all the toys, is he mummmeee?", or "Can you get me a fire station, not a toy one, a real one to live in?"
Sometimes it's just an observation from his day, like "Harry in my school did a poo at the table today" or "Miss in school is four like me", but you can't get away with ignoring him. Oh no, you must for the love of God answer these and any follow up questions or get no sleep at all whatsoever.