Preheat the oven to 325 degrees F. Lightly butter a 2-quart oven-safe dish.
Cut the top off of the garlic head to expose the garlic. Put the head on a piece of aluminum and drizzle with olive oil. Sprinkle with salt and pepper and close. Place the garlic into the oven and roast until soft, about 45 minutes. Remove from the oven and open to cool slightly before using.
Bring the chicken stock, 1 1/2 cups water and 1 teaspoon salt to a rolling boil in a large pot over high heat. Add the grits and stir well with a whisk. Cook, stirring constantly, until the liquid is absorbed, about 5 minutes. Remove from the heat and stir in the butter. Add the eggs while whisking quickly, and fold in 3 tablespoons of the roasted garlic, the cheeses, jalapenos, cayenne, 1/2 teaspoon black pepper and white pepper. Once the grits are thoroughly combined and smooth, transfer to the prepared baking dish and cover with foil.
Bake for 1 hour 20 minutes, then remove foil and cook 10 minutes longer to brown the top.