Scatter the parsnips over a baking sheet and toss them with about 1 tablespoon EVOO and season them with salt and pepper. To stuff the chicken breasts, carefully loosen the skin from the meat with your fingers, creating a pocket. Divide the stuffing into 4 equal portions and stuff it under the skin into the pocket, taking care not to rip the skin. Place the stuffed chicken breasts on top of the parsnips and drizzle each breast using about 1 tablespoon of EVOO and season them with salt and pepper. Roast the chicken and veggies until golden brown and cooked through, 35-40 minutes depending on how big your chicken pieces are. Transfer the chicken to a plate to rest and turn the parsnips out into a large mixing bowl. Using a potato masher, smash up the parsnips, thinning them with a little stock as needed, until they're the consistency of chunky mashed potatoes.
When the chicken is almost done roasting, place a medium-size skillet over medium-high heat with 1 turn of the pan of EVOO, about 1 tablespoon. Add the fennel to the skillet and cook until it starts to get tender, 3-4 minutes. Add the green apples, some salt and pepper, and continue to cook for another 3 minutes or until all the veggies are tender. Remove the pan from the heat, roughly chop up the fennel fronds and toss them into the pan.
Serve a stuffed chicken breast a scoop of sautéed fennel and apples on top and some parsnip mash alongside.