One of the first disillusioning discoveries the home cook makes is that softening and browning onions takes a lot longer than the recipe books state. You have to fuss over them as well, or else bits of onion stick to the pan, and burn.
Butter, which itself browns easily, helps the browning process. But you need quite a lot of butter for even one onion, because of the separation of the solids and liquid, which evaporates. That does not happen to oil; so, to ensure that there is lubrication in the pan, I usually brown onions in a butter/oil mixture. They need regular stirring, because the oil will not protect the butter from burning. Turning up the heat in an effort to speed the process is a bad idea.
Brown onions enrich the sauce in a stew or a curry. Last night, I made a chicken curry, of the kind that is likely to feature leftover turkey in many homes at the end of this month. It is the kind of dish -- makeshift, and hot -- that I love to prepare when I'm cooking for myself.
I browned my onion, and threw in a chopped clove of garlic and a finely chopped (small) knob of ginger, along with 1/3 tsp cumin seeds and 4 cardamoms -- both crunched a bit in a mortar. After another couple of minutes of stirring and frying, I poured in the remains of some roast chicken gravy (I had about 125 ml) and a ladleful of stock, along with a little salt, 1/3 tsp turmeric, and 1/3 tsp chilli powder. I let this bubble for five minutes. Then I added leftover chicken, and simmered for five minutes longer.
Browning the onions apart, this meal -- including some boiled rice -- was very quick and simple to prepare. It was far nicer than any takeaway I've had recently. The ginger was the key ingredient, lifting but not dominating all the other flavours.