"I use 'walnut polishing' with kitchen wooden stuff because its natural which ensures that there would be nothing toxic in your spoons.
I do like this: I brake a walnut in some pieces, put them in a piece of cloth, make a twist in the fabric, and finally rub on the wood surface making pressure so the oil pass through the fabric.
The walnut oil will deepen the grain colour wood.
Just like that!"
Sounds like a very natural and traditional method of oiling. Give it a try - let me know how you get on.