Dice onion and bell pepper; add to dutch oven with a touch of saute oil and a pinch of salt. Sweat for 3-4 minutes. As it sweats, mince jalapeno and garlic. Add to dutch oven along with cumin/chili powder/oregano, cook for another minute.
Add drained beans and tomatoes to the dutch oven. Adjust heat and simmer for 15 minutes.
As sauce cooks, prepare eggs to your liking. If you want to poach in the sauce (and you do!) use your large spoon to make small wells in the sauce and crack the eggs into each well. Cover the pan and cook for 5-8 minutes, or until the eggs are done to your liking.
Once sauce is finished and eggs are cooked, top with cheese and serve along with warmed tortillas.