Heat a large, deep skillet or sauté pan over medium-low heat. Add half of the extra-virgin olive oil. When the oil is hot, add the finely chopped shallot and cook, stirring, until slightly softened and not browned, about 2 minutes.

Add the chopped broccoli, minced garlic, kosher salt, and black pepper to the skillet. Sauté, stirring occasionally, until the broccoli is crisp-tender, about 3 to 4 minutes. Transfer the broccoli and shallots to a bowl and set aside.

Add the remaining olive oil to the same skillet. Add the uncooked quinoa and toast, stirring often and scraping the bottom of the pan, for 1 minute.

Pour in the low-sodium vegetable or chicken stock (1 1/2 cups). Increase heat to bring the mixture to a gentle boil, then reduce heat to low. Cover and simmer until the quinoa is tender and most of the liquid is absorbed, about 12 minutes.

Stir in the rinsed and drained white beans and the reserved broccoli-and-shallot mixture. Cook, stirring, until everything is heated through, about 2 minutes.

Remove the skillet from the heat. Stir in the freshly grated Parmesan until combined. Sprinkle with chopped fresh parsley, taste, and add additional salt or pepper if desired. Serve hot with extra Parmesan if you like.