SET oven rack to the center position; PREHEAT oven to 350°F; BUTTER a 3-quart baking dish.
DIVIDE an 8 ounce block of Monterey Jack cheese in half; cut each half into 6 equal slices, for a total of 12 cheese slices (if using a large brick of cheese, cut 1/2" slices into diagons). Shred the remaining 16 ounces cheese (or use pre-shredded Monterey Jack cheese).
DRAIN one 27-ounce can whole green chiles; BLOT chilies well; PLACE into buttered baking dish,.
STUFF 12-16 green chiles with one wedge of cheese; ARRANGE stuffed chiles single-layer, overlapping if necessary (arrange wide ends of chiles beside narrow ends of following chile until all chiles are used).
BLEND the dry ingredients of the batter first in a medium bowl (1/3 cup flour, 4 tablespoons powdered parmesan cheese, 1 teaspoon baking powder, 1/2 teaspoon salt, 1 teaspoon crushed dried basil, and 1/4 teaspoon crushed dried rosemary; WHISK in 8 beaten eggs with 1 1/4 cups milk until batter is smooth.
STIR the saute mixture into the batter; POUR the batter over chiles in baking dish; SPREAD 12 ounces (3 cups) shredded cheese evenly over the batter mixture.
BAKE casserole uncovered in a 350°F oven for 35 minutes; LEAVE oven on.
REMOVE casserole from oven; SPREAD one 14-ounce jar pizza sauce evenly over the top; SPRINKLE evenly with the remaining 4 ounces (1 cup) shredded cheese; RETURN to oven and continue baking uncovered for 10 minutes.
ALLOW to cool and set for 5-7 minutes before cutting.