Place the uncooked rice into a 3-1/2-quart Dutch oven with a heavy lid. Add the vegetable stock and a pinch of salt. Bring the broth to a boil over high heat. Immediately turn down the heat to simmer and put the lid on. Simmer for 20 minutes.
Heat 1/2 inch of oil in a 2-quart saucepan over medium high heat. When the oil is hot, add the shallots. When the shallots are brown, in just a couple of minutes, remove them from the pan with a slotted spoon to a paper towel-lined plate and season with salt and pepper. Set aside.
When the rice is done, quickly add the peas. Don't stir them; just leave them on top of rice to steam. Cover the pot and let simmer for 10 minutes.
Fluff the rice/peas with fork. Spoon mixture into bowls, sprinkle with the chives and parsley, and finally with the shallot garnish. Serve while hot.