Preheat the oven to 400 degrees F (200 degrees C).

Season pork with salt and pepper. Heat oil in a large skillet over medium-high heat and cook pork until browned on all sides, 5 to 8 minutes. Remove from skillet and set aside.

Combine Gruyere cheese, cream, eggs, nutmeg, salt, and pepper in a bowl and stir together.

Slice pork and layer pork, potatoes, mushrooms, and carrots into a casserole dish. Pour egg-cheese mixture on top.

Bake in the preheated oven until cooked through and lightly browned on top, about 1 hour. Sprinkle with parsley to serve.