Cook the bulgur according to package directions or click here to see how, using the water and the vegetable broth. Once cooked, fluff with a fork, then if you are planning this to be a room temperature side spread the hot bulgur on a rimmed baking sheet to cool. If you want it to be a hot side, then keep the lid on until the onion is cooked and everything is ready to be tossed together.
While the bulgur is cooking heat the olive oil in a large skillet over medium heat. Add the onions, season with salt and pepper and cook for about 20 minutes, stirring often, until the onions are tender and caramelized. Adjust the heat so that the onions are cooking and browning quite slowly – that’s how they will get even sweeter and gently caramelized. Stir in the parsley.
In a large bowl stir the cooled bulgur with the onion-parsley mixture. Taste and adjust seasoning as needed. Add more olive oil by the tablespoon if the mixture seems dry.