Drain peppers; halve lengthwise and remove seeds.
Cut Monterey Jack cheese into strips to fit inside peppers.
Wrap each pepper around a strip of Monterey Jack cheese; place in a greased 10x6x2-inch baking dish.
Combine eggs and milk; beat in flour, baking powder, and salt till smooth.
Pour over peppers.
Sprinkle Cheddar cheese atop.
Bake at 350° till golden, about 30 minutes.