Heat olive oil in a deep skillet over medium-high heat. Once hot, add onion and saute 2 minutes, then add chicken and cook 2 1/2 minutes stirring occasionally. Add garlic and saute 1 minute longer (chicken should be cooked on outsides but inside doesn't need to be fully cooked through at this point because it will boil and simmer).
Add in broth, quinoa and thyme and season with salt and pepper to taste. Bring to a full boil then cover, reduce heat to a simmer and cook 12 minutes.
Then quickly lift lid, sprinkle broccoli over top, recover and simmer about 8 minutes longer or until quinoa and broccoli have cooked through (it may have a little broth in the bottom still at this point and you can carefully drain it off if desired, just don't pour everything down the drain!). Sprinkle cheese over top, cover and heat 1 - 2 minute until cheese has melted.