Toddler friendly all purpose (peanut free) sauce to put on everything from steamed veggies to brown rice

Washington Post has a great quick stir-fry sauce that's great on veggies and brown rice and can be made ahead. Here's the link: https://www.washingtonpost.com/recipes/quick-stir-fry-sauce/15473/

One liked sriracha, the other liked anchovy/lemon/olive oil. And, since they were toddlers, this changed from day to day, hour to hour. Without warning.

My 5 year old would put ketchup on all those things. My 2 year old is happy with garlic butter.

Teriyaki sauce http://www.food.com/recipe/restaurant-teriyaki-sauce-133751

Ranch dressing

It depends on what your toddler likes.

For several billion people on this planet, soy sauce would be the condiment of choice.

Here in the USA, maybe it would be ketchup.

In New Zealand, it might be plum sauce:

http://luckypeach.com/recipes/plum-sauce-92/

All are peanut free. Good luck.