Heat the olive oil in a large, fairly deep skillet over medium-high heat. When the oil is hot, add the chicken and spread it into a single layer. Season with salt and pepper. Let it brown for about 2 minutes before moving it. Add in the shallots and garlic and sauté another 2 minutes (chicken should be cooked on outsides but inside doesn't need to be fully cooked through at this point).

Stir in the chicken broth, pesto and quinoa. Season with a little more salt and pepper. Bring to a full boil then cover with a lid and reduce the heat to a simmer. Cook 12 minutes.

After 12 minutes add in the broccoli and spinach, recover and simmer about 8 minutes longer or until quinoa and broccoli have cooked through (if there is still excess broth in the bottom at this point, you can use a spoon to carefully drain it off if desired). Taste for seasoning then sprinkle the mozzarella cheese over top. Cover and heat 1 - 2 minute until cheese has melted.