Preheat the oven to 375°F.
Dice the chicken breast into bite-sized pieces. Chop the carrot, parsnip, celery, and onion into uniform cubes.
In a large oven-safe skillet, heat the olive oil over medium heat. Sauté the onion until translucent, then add the chicken pieces and cook until lightly browned.
Add the chopped carrot, parsnip, and celery to the skillet and cook for another 5 minutes, stirring occasionally.
Sprinkle the whole wheat flour over the mixture and stir well to coat the ingredients evenly. This will help thicken the sauce.
Slowly pour in the low-fat milk while stirring continuously to avoid clumps. Allow the mixture to simmer for 3-4 minutes until it begins to thicken into a creamy sauce.
Season with your preferred herbs and spices (such as thyme, rosemary, salt, and pepper) to taste.
Transfer the skillet into the preheated oven and bake for 15-20 minutes until the vegetables are tender and the flavors meld together.
Remove from the oven, let cool slightly, then serve warm.