Heat a large, deep skillet or sauté pan over medium low. Add half the oil to the skillet. Once the oil is hot, add the shallot. Cook until slightly softened, about 2 minutes, not allowing the shallot to brown. Add the broccoli, garlic, salt, and pepper. Sauté until the broccoli is crisp-tender, about 3 to 4 additional minutes. Remove the broccoli and shallots from the skillet and set aside.

Add the remaining oil to the skillet. Add the quinoa and let toast for 1 minute, stirring often and scraping up along the bottom of the pan. Add the chicken stock. Bring to a boil, and then lower the heat. Cover and let simmer until the quinoa is tender, about 12 minutes. Stir in the white beans and broccoli mixture and cook until warmed through, about 2 additional minutes. Stir in the Parmesan and sprinkle with fresh parsley. Taste and add additional salt or pepper as desired. Serve hot, with additional Parmesan.