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, garlic, and oregano, stirring until cheese melts; let 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 baking dish from oven. Increase oven temperature to 400°.
Sprinkle remaining 1 1/2 cups cheese, ham, and chiles evenly over grits crust. Whisk together remaining 6 eggs and 1/2 cup milk; pour into baking dish.
Stir together remaining 1 cup milk and next 3 ingredients; spoon evenly over egg mixture, slightly spreading with back of a spoon. (Baking mix mixture will be very thick.)
Bake at 400° for 35 minutes. Cool 10 minutes; cut into squares. Serve with salsa, if desired.
*2 cups (8 ounces) shredded Cheddar cheese may be substituted.