In a large skillet or pot with a tight-fitting lid, heat the oil and 1 tablespoon of the butter over medium heat. Add the chicken and season it liberally with salt and pepper.
Cook the chicken for about 5 minutes, or until cooked through. Transfer the chicken to a plate and set it aside.
To the same skillet, melt the remaining butter. Add the onion and celery and cook for 3-4 minutes until softened.
Add the garlic, thyme, rosemary, and crushed red pepper flakes. Cook for another minute until fragrant.
Stir in the quinoa and broth. Increase heat to high and bring mixture to a boil. Reduce heat to low, cover, and cook for about 15 minutes, until most of the liquid has been absorbed by the quinoa.
Add the broccoli and return the chicken to the skillet. Cover and cook for another 5 minutes, or until the quinoa has absorbed all of the liquid.
Stir in the lemon juice and sprinkle with parsley. Serve warm.