What can I use to seal a wooden spoon with so it is still ok to cook with?

As a woodworker I've come to find that what is traditionally used is mineral oil. However, you would want to do this to bare wood. It penetrates the grain to protect the wood and won't become rancid over time. Using laquer or varnish may chip off when exposed to high temperatures and if exposed to direct flame will leave an awful taste to your cooking. I also highly recommend not using them for cooking after being painted for the very same reasons that I've mentioned with using laquer or varnish. My work can be seen at wegnerwoodworkings.com

You could do as the Chinese and Japanese do with their lacquerware and use lacquer, or even shellac, although normal shellac will not standup to water well. Some of the acrylic lacquer products available at your local hardware store might be useful, and not give off tastes, particularly if you bake them at low temperature to hard dry them, prior to use.

But really, it's a lot easier to just sanitize wooden spoons regularly with a little chlorine bleach [which will also keep them from browning], and re-apply vegetable oil (if you like) as necessary, to prevent water penetration. Given the low cost of wooden spoons, they're hardly worth doing a lot to preserve.

PAULSC is right, the quickest way to brown your spoons it by running them in the dishwasher. Natural wood should be cleaned by hand.

If you really want to seal it. You could try food-grade silicone.

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Use laquer