New answers tagged caramelization
Carrots and onions have different cooking times, so no, you can't throw them together. What I would do is cut the carrots as small as the onions (just for aesthetic purposes), start stewing the carrots in a closed pot first and season them as you like, and when they're nearly done, add the onions and caramelise them normally while they're stewing together ...
You do not add fat to sugar when caramelizing it, you add it to the pan dry. Sugar has water suspended in it, and it comes out when heated. The caramel will transfer the heat to the onions just fine - anyone who's ever gotten splattered with hot caramel will attest to that.
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