Cut a lengthwise slit from stem to bottom of each chile. Make a crosswise incision at stem end, forming a T.
Pry open enough to hold back long cuts (to expose ribs and seeds), then devein and seed using tip of a paring knife and kitchen shears.
Stir together cheeses, hot sauce, 1/4 teaspoon pepper, and 3/4 teaspoon salt.
Fill chiles with cheese mixture, pressing seams closed after filling, so that cheese is compacted and chile retains its shape.
Lightly beat eggs in a small shallow bowl. Stir together bread crumbs, oregano, and 1/4 teaspoon each of salt and pepper in another shallow bowl.
Dip chiles in egg, letting excess drip off, then coat with bread crumbs, transferring to a work surface. Repeat coating with egg and crumbs to form a second layer.
Heat 2 inches oil to 325°F in a medium saucepan. Fry chiles in 3 batches, stirring occasionally, until golden brown all over, 5 to 6 minutes per batch.
Transfer to several layers of paper towels to drain. Return oil to 325°F between batches.
