Heat oil in a Dutch oven over medium-high heat. Add onion; sauté 2 minutes. Add bacon; sauté 5 minutes. Add peas and next 4 ingredients (peas through bay leaf); bring to a boil. Reduce heat; simmer, partially covered, 30 minutes or until tender. Discard bay leaf.
Combine broth, quinoa, salt, and black pepper in a saucepan; bring to a boil over medium-high heat. Cover, reduce heat, and simmer 30 minutes or until done. Add quinoa mixture to pea mixture, and stir. Sprinkle with green onions and chopped parsley.