Bring first 5 ingredients to a boil in a medium saucepan; gradually stir in grits. Cover, reduce heat, and simmer, stirring occasionally, 5 to 7 minutes. Add 1/2 cup cheese and garlic, stirring until cheese melts; let mixture cool 10 to 15 minutes. Stir in 2 eggs, and pour into a lightly greased 13- x 9-inch baking dish.
Bake at 350° for 20 minutes; remove from oven. Increase oven temperature to 400°.
Sprinkle remaining 1 1/2 cups cheese, ham, and green onions evenly over grits crust. Whisk together remaining 6 eggs and 1/2 cup milk; pour into crust.
Stir together remaining 1 1/2 cups milk and baking mix; pour over egg mixture, spreading to edge of dish with back of spoon.
Bake at 400° for 35 minutes. Cool 10 minutes, and cut into squares.