Heat the olive oil in a large pot over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion and garlic to the pot. Cook for 3 minutes until the onion begins to soften.
Stir in the parsnips and Brussels sprouts so they coat in the oil and pan juices.
Pour in the chicken broth. Add the Dijon mustard, maple syrup, thyme, salt, and black pepper. Stir until the mustard and syrup are fully blended into the broth.
Bring the stew to a gentle simmer. Cover the pot and cook for 25 minutes, or until the chicken is cooked through and the parsnips are tender.