Bring the milk and water to a boil over high heat in a large nonstick saucepan. Whisk in the grits, salt, and pepper and return to a simmer. Reduce the heat to low, cover the saucepan, and cook the grits until tender and thick, stirring frequently, about 30 minutes.

While the grits are cooking, heat the olive oil in a large skillet over medium-high heat and saute the sausage until browned, 4 to 6 minutes. Add the onion, bell pepper and Essence and cook, stirring occasionally, until the vegetables are soft and golden, about 4 minutes. Stir in the garlic and cook for 2 minutes longer, then remove from the heat and set aside.

Preheat the oven to 350°F and lightly grease a 9- by 13-inch casserole dish.

When the grits are tender and thickened, stir in two-thirds of the grated cheddar, the grated pepper jack, heavy cream, and butter. Add the eggs and green onions, then stir in the reserved sausage-vegetable mixture. Spoon the grits into the prepared casserole dish, and top with the remaining cheddar. Bake in the center of the oven until the casserole is lightly golden on top and set, about 45 minutes. Let stand for 5 to 10 minutes before serving.