Grease an 8 by 8-inch square cake pan or rimmed baking sheet with the butter, line with parchement or wax paper and grease again. Set aside.
In a large, heavy saucepan, bring the water to a boil. Slowly add the grits, salt and pepper, whisking constantly. Bring to a boil, then reduce the heat to low and simmer until thickened, about 20 minutes, stirring occasionally.
Remove from the heat, add the cheese, green onions, and garlic, and adjust the seasoning to taste. Turn out the mixture onto the prepared baking sheet and using an offset cake spreader or rubber spatula, spread evenly across the bottom. Refrigerate until completely cooled and firm, at least 1 hour. Cut the grits into squares and refrigerate until ready to work.
In a large, heavy skillet or saute pan, heat 1/2 cup of the oil to 350 degrees F.
Combine the flour and Essence in a shallow dish. Combine the eggs and milk in another shallow dish, whisking to combine.
Dredge the squares in the seasoned flour, dip into the egg wash, and then back into the flour, 1 at a time. Fry in batches, turning, until golden brown, 2 to 3 minutes, adding more oil as necessary. Remove with a slotted spoon and drain on paper towels. Season fried grits lightly with Essence.