Mix the baking mix and yeast and stir in the hot water. Turn the dough onto a well-floured surface and knead until smooth, about 20 times. Let the dough rest a few minutes.
While the dough is resting, cook and stir the meat and onion in a large skillet until the onion is tender and the meat is brown. Drain off the excess fat. Stir in the tomato sauce, oregano leaves, and pepper and set aside.
Divide the dough in half. Roll each half on an ungreased baking sheet into a 13 x 10-inch rectangle or on a pizza pan 12 inches in diameter. Pinch the edges to make a slight rim. Spread the meat mixture almost to the edges. Top with the green pepper and cheeses. Bake until the crust is brown and the filling is hot and bubbly, 15 to 20 minutes.
Cut into squares or wedges and serve.