Heat 3 tablespoons of oil in the pot over medium heat. Add the onions and cook stirring the onions until they become translucent.
Once the onions have become translucent, add the corn, and cook stirring to heat it through. Stir in the rice, making sure it's all covered in a light oil film. This will help fix the starch and produce rice that is not too sticky (graneado).
Pour in the vegetable broth and stir the rice.
Simmer uncovered, and stir regularly to avoid excessive sticking, always scraping as much of the rice at the bottom as possible.When almost all the liquid has evaporated cover with a tight-fitting lid and simmer over low heat for 10 minutes.Uncover and stir, moving the rice from the bottom to the top. Cover again and cook for 10 more minutes. Try the rice, it should be firm but cooked through (see notes). If necessary, cover and simmer for another 5 minutes over very low heat.
Uncover, add the remaining oil, and stir. Mix in the parsley and remove from the heat.
After removing it from the heat, scoop the rice right away into a serving bowl. Scrape the rice at the bottom (concón) and serve alongside as a special treat. See above the recipe for serving suggestions.
Our recipe for vegetable broth yields unsalted broth. Add enough salt to your liking, then heat to boiling point before adding to the rice. Do not add cold liquid to the rice, or it may not cook properly.This is a recipe that definitely goes better if the rice is loose and non-sticky (graneado). This is why I cook the rice a bit in the oil before adding liquids.