Season the chicken pieces with salt and pepper. Heat the olive oil in a large skillet over medium-high heat. Add the chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set it aside.
In the same skillet, add the chopped onion and sauté until softened, about 4-5 minutes (add more olive oil if the onion sticks). Add the minced garlic and cook for another minute. Stir in the diced apples and cook for 3-4 minutes, until they start to soften.
Sprinkle the flour over the onion and apple mixture, stirring to coat everything evenly. Cook for 1-2 minutes to remove the raw flour taste.
Slowly pour in the chicken broth and apple cider, stirring constantly to prevent lumps. Bring the mixture to a simmer, and cook until the sauce thickens, about 5 minutes.
Stir in the heavy cream, fresh thyme, and ground nutmeg. Return the cooked chicken to the skillet and stir to combine. Season with additional salt and pepper to taste.
Remove the skillet from the heat and gently fold in the pieces of Brie cheese, allowing them to melt slightly into the mixture. Stir until mixed.
If you're pairing with biscuits, you're done! If you want to cover it, use a sheet of puff pastry over the top of the filling, crimp with a fork, brush with beaten egg, and bake in 400°F oven for 20-25 minutes.