Heat oil in a cast-iron skillet over medium-high heat; saute onion until lightly browned, 5 to 10 minutes. Add ground beef; cook and stir until beef is browned and crumbly, 5 to 10 minutes. Mix pinto beans and black beans into beef mixture.
Sprinkle Mexican cheese blend over beef-bean mixture; stir. Mix diced tomatoes with green chile peppers into beef-bean mixture.
Mix corn bread mix, milk, and eggs together in a bowl until batter is smooth. Spread batter over top of beef-bean mixture.
Bake in the preheated oven until a toothpick inserted in the center of the cornbread comes out clean, 15 to 20 minutes.