Preheat oven oven to 350 degrees.
Brush baking sheet with 1 Tbsp of olive oil. Place 4 of the tortillas on the baking sheet and top each with ¼ cup of cheese. Cover each tortilla with one of the remaining 4 tortillas. Bake at 350 for 5-6 minutes or until lightly browned.
Meanwhile, in a skillet, heat the remaining 1 Tbsp olive oil and cook onion until tender. Mix in black beans and green chilies. Use a potato masher or back of a fork to partially mash the mixture.
Remove tortilla pizzas from the oven and top with the bean mixture spreading evenly. Top each pizza with 2 Tbsp of cheese.
Return to oven and bake until cheese melts, about 10 minutes.