Preheat the oven to 350 degrees F. Spray a 10-inch ovenproof skillet with nonstick cooking spray.
In a large bowl, whisk together the eggs with the milk and baking mix. Stir in the reserved au gratin and ham. Pour the mixture into the skillet. Place in the oven and continue to cook until the center is firm and the top is golden, 20 to 25 minutes.
Root Vegetable Au Gratin:
Preheat the oven to 350 degrees F. Spray a 9 by 9-inch baking dish with cooking spray.
In a small pot, heat the milk with the thyme over medium-low heat until hot.
In a medium saucepan over medium heat, melt the butter with the canola oil. Add the garlic and cook 1 minute. Add the flour and cook stirring constantly until the flour is lightly golden brown, about 2 minutes. Slowly whisk in the hot milk. Bring the mixture to a simmer and cook until very thick. Stir in the Cheddar, pumpkin pie spice and salt and pepper to taste.
Coat the bottom of the prepared baking dish with a thin layer of the sauce. Place one layer of carrots slightly overlapping in the bottom of the baking dish. Top with an overlapping layer of the parsnips. Pour a third of the sauce over top. Repeat with two more layers each of the carrots and parsnips, ending with the sauce.
In a small bowl, stir together the breadcrumbs, Parmesan, parsley and salt and pepper to taste. Evenly sprinkle over the top of the gratin.
Bake until the gratin is bubbling and the topping is browned, and when pierced through the vegetables yield easily, about 1 1/2 hours. If the top begins to brown too quickly, cover with foil. Let rest for 10 minute before serving.
Brown Sugar Glazed Ham:
Preheat the oven to 325 degrees F.
Place the ham in a roasting pan fat-side up. Score the fat with a crisscross pattern. Cook the ham for about 1 hour to allow the scored fat to open up.
In the meantime, in a small saucepan over medium heat, stir together the brown sugar, apple jelly, mustard, vinegar, ginger and garlic along with 2 tablespoons water. Bring to a simmer and cook for about 2 minutes until it has a smooth syrupy consistency.
Remove the ham from the oven. Generously brush the ham with half of the glaze. Place back in the oven and bake an additional 1 hour and 30 minutes, basting with the remaining glaze every 20 minutes. If the ham starts to get too brown, cover with foil. Remove from the oven, cover and allow the ham to rest for 30 minutes before slicing and serving.