Step 1

Preheat the oven to 400 degrees F. Butter two 9-by-13-inch baking dishes with 1 tablespoon butter each.

Step 2

Stir together the Parmesan, thyme leaves, 1/3 cup of the heavy cream, half of the garlic, 1/2 teaspoon salt and some pepper in a medium bowl. Add the Yukon gold potatoes, toss to coat and spread evenly in one of the prepared baking dishes.

Step 3

Stir together the brown sugar, maple syrup, cinnamon and 1/2 teaspoon salt in a medium bowl. Add the yams, toss to coat and spread evenly in the other prepared baking dish.

Step 4

Cover both baking dishes with aluminum foil and bake for 20 minutes. Remove the foil and continue to bake until the potatoes and yams are tender when pierced with a fork, an additional 5 to 8 minutes. Let cool slightly. Reduce the oven temperature to 325 degrees F.

Step 5

Stir together the cream cheese, Gruyere, nutmeg, remaining 1/4 cup heavy cream, remaining garlic, 1/2 teaspoon kosher salt and a few cracks pepper in a medium bowl. Add the spinach and stir to combine and coat.

Step 6

Position the ham flat-side down on a cutting board with the fat cup facing up. Using a sharp knife, cut 1/2-inch-wide slices across the length of the ham about three-quarters of the way down through the ham.

Step 7

To assemble: Fill the space between the first 2 slices of ham with some of the creamed spinach, pressing to even out the filling. Skip 3 slices (so there are 2 spaces in between) and fill the next space with more of the creamed spinach. Continue in the same manner, dividing the creamed spinach evenly among every third space. Fill each space next to the creamed spinach with a layer of the scalloped potatoes, dividing the scalloped potatoes evenly among every third space. Fill each space next to the scalloped potatoes with a layer of the candied yams, until all the spaces are filled.

Step 8

Place the ham on a rack in a roasting pan, add 2 cups of water to the bottom and tent the ham loosely with aluminum foil. Bake until the ham is heated through and the potatoes are slightly golden, about 1 hour 15 minutes.

Step 9

In the meantime, melt the remaining 2 tablespoons butter in a skillet over medium-low heat. Add the shallot and cook until softened, about 5 minutes. Add the honey and heat through, whisking to combine. Season with a few cracks of pepper.

Step 10

Remove the foil and brush about half the glaze over the top of the ham. Return to the oven until the glaze is thick, glossy and deep golden, about 10 minutes more. Carefully transfer to a platter and pour the remaining glaze over top.