Place a pizza stone on the bottom rack of the oven. Preheat oven to 450 degrees F.
In a small saucepan heat oil over medium-high heat. Add onion, garlic, and season with salt; cook for 3 minutes or until onion and garlic are tender. Stir in chili powder and cumin; cook for 1 minute more. Remove from heat; stir in beans and 3 tablespoons of the water. Transfer mixture to a food processor. Cover and pulse until bean mixture is spreadable but still chunky, adding more water if necessary to make a spreadable mixture.
Working with one tortilla at a time, evenly spread a thin layer of the bean mixture on tortilla. Top with 1/2 cup of the cheese and one-fourth of the carnitas. Transfer topped tortilla to the pizza stone. Bake for 4 to 5 minutes or until cheese is bubbly and edges are golden and crisp.
Transfer the tortilla to a cutting board; let cool for 1 minute. Top with a bit of the shredded cabbage and cilantro. Serve alongside the salsa and cut each Mexican pizza into wedges before serving.