Divide jack cheese evenly among chiles, folding or tucking cheese inside.
Arrange chiles side by side in bottom of a greased, shallow 1 1/2-quart baking dish.
With an electric mixer beat eggs until thick and foamy then add milk, flour, and baking powder; beat until smooth as possible.
Pour egg batter over chiles, moistening evenly the surface of all chiles.
Sprinkle with Cheddar cheese.
Bake uncovered in a 375° oven for about 30 minutes or until casserole is puffed and appears set when gently shaken.
Just before casserole is ready, heat marinara sauce to simmering.