Lay chiles in a single layer on a baking sheet. Cook about 4 in. from broiler until chiles are blistering and black, about 5 minutes. Turn chiles over and broil until blistering and black all over, about 5 minutes. Put chiles in a large metal bowl and cover with foil or plastic wrap.
Let sit 15 minutes.
Peel chiles and discard skins.
Cut off stem ends and discard; remove seeds. Set chiles aside on layers of paper towels to dry.
Meanwhile, in a large frying pan over medium-high heat, cook chorizo, stirring occasionally to break up the meat, until cooked through, about 4 minutes.
Preheat oven to 37
In a large bowl, mix chorizo, cotija, and oregano. Stuff chiles with mixture and lay them in an 8- by 12-in. baking dish.
In a large bowl, whisk eggs until they are thoroughly broken up and uniform in color and texture.
Whisk in flour, baking powder, and salt.
Sprinkle chiles with 1/2 the jack cheese.
Pour egg mixture over chiles and sprinkle with remaining jack.
Bake until top starts to brown and the eggs are set but still soft, about 30 minutes.
