For how long should I cook onion paste? I followed a recipe the other day that involved cooking "Onion Paste" till Golden Brown. There were no details on how to make it so I assumed it was just "Take the onions and make a puree".

I cooked it for like 10 minutes but it did not change color. I continued on with the recipe as I was afraid that if I cook it longer, it may turn bitter. Usually when I cook chopped onions, they become golden brown in 10 minutes.

I am wondering if I did something wrong? Please note that I also added some water in the mixer while making the puree.
Pureeing onions makes them release a lot more of their water than just chopping them, and if you added extra water on top of that, you probably had a very wet paste. That makes it take a lot longer to cook - while you're just boiling away water, it's not hot enough to brown much.

So cook it as long as it takes - it's not going to become bitter. (If anything, it'll get sweeter!)  And if you want it to cook faster, don't add extra water. If you watch carefully, you can also turn the stove up hotter at the beginning to boil off water faster, then reduce the heat once it's drying out enough to avoid burning it.

If whatever you used to make the puree doesn't work well without the extra water, you can still use it; just know that it'll make it take longer to cook. Otherwise, you could try grating the whole onion on a cheese grater, which does a surprisingly good job - it'll still be really juicy though!