For the grits:

In a large heavy saucepan, bring the water and salt to a boil. Stirring with a wooden spoon, add the grits in a slow, steady stream and cook, stirring frequently, until thickened and tender, 45 minutes to 1 hour. Remove from the heat and add the butter, Parmigiano, and white pepper, stirring until combined. Add the egg and stir to incorporate.

Meanwhile, preheat the oven to 375°F. Butter eight to ten 4- to 6-ounce ramekins.

Divide the grits among the buttered ramekins, place in a baking pan, and add enough hot water to the pan to come halfway up the sides of the ramekins. Cover with foil and bake for 15 minutes. Remove the foil and bake for about 20 minutes longer, or until the tops are crusty and beginning to brown.

For the sauce:

In a medium sauté pan, combine the wine, vinegar, shallots, bay leaf, chile pepper, and ham and bring to a boil. Cook until only 1 tablespoon of liquid remains. Reduce the heat to low and stir in the crèam. Whisk in the butter bit by bit, adding each new piece as the previous one is incorporated.

Strain the sauce into a saucepan. Add the Parmigiano and season with salt and pepper, lemon juice, and hot sauce to taste. Keep warm.

For the garnish:

Heat the oil in a small sauté pan over medium-high heat. Add the julienned ham, mushrooms, and shallot and cook until the mushrooms are barely tender, 3 to 4 minutes.

Unmold the grits onto serving plates and turn browned side up. Ladle a little sauce around the grits and top with the mushrooms and ham. Garnish with thyme leaves.