Preheat oven to 400 degrees F.
In a large skillet, melt the 1/2 cup unsalted butter over medium-low heat. Continue to cook the butter, stirring frequently until brown bits form on the bottom of the pan and the butter starts to brown. Once you see this process occurring, remove the pan immediately from the heat. Stir in the bourbon and maple syrup, and set aside.
In another large skillet, melt the 3 tablespoons unsalted butter over medium heat. Add the shallot and cook until tender, about 4 minutes. Whisk in the flour and cook until lightly golden, about 2 minutes. Whisk in the vegetable stock, heavy cream and whole milk. Bring to a simmer, and simmer for about 5 minutes or until the sauce has thickened substantially. Stir in the salt, pepper, nutmeg, cinnamon, parmesan cheese, and thyme. Remove from heat.
Spoon a thin layer of maple bourbon brown butter on the bottom of a large cast iron skillet. On the top of that, spoon a thin layer of the cream sauce. Assemble your sweet potato rounds in an even layer (see images) in your cast iron skillet. Spoon the rest of the cream sauce over top, filling all of the nooks and crannies. Also, spoon on the remaining maple bourbon brown butter. Cover the pan with foil and place it in the oven. Bake for 30 minutes. After 30 minutes, remove the foil and cook for an additional 20 minutes. Remove from heat and let stand for about 5 minutes before serving.
Garnish with fresh parsley and toasted pecans if desired. Enjoy!