Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Season both sides of the chicken breasts with salt and black pepper.
Add the chicken breasts to the skillet and cook for 4-5 minutes on each side until golden brown but not fully cooked through. Remove chicken from the skillet and set aside.
Reduce heat to medium and add butter to the same skillet. Once melted, add minced garlic and sauté for 1 minute until fragrant.
Add diced carrots and celery to the skillet and cook for 3 minutes, stirring occasionally.
Stir in rinsed quinoa, dried thyme, and crushed red pepper flakes, coating the quinoa with the garlic butter mixture.
Pour in the chicken broth and bring the mixture to a boil.
Return the chicken breasts to the skillet, placing them on top of the quinoa mixture.
Cover the skillet with a lid, reduce heat to low, and simmer for 15 minutes until the quinoa is tender and the chicken is cooked through (internal temperature 165°F).
Remove the lid and stir in the chopped baby spinach until wilted, about 1-2 minutes.
Sprinkle chopped fresh parsley over the dish before serving.