In a cast-iron skillet, add oil, onion, jalapeños, cumin, chili powder and pepper. Saute until veggies are soft.
Make a garlic paste: On a cutting board add salt to minced garlic. Chop and smash garlic and salt back and forth several times.
Add paste to skillet and saute until soft, about 3 to 5 minutes. Add tomato puree, water and cilantro. Bring to a boil, then reduce heat to simmer. Cover and cook for 15 minutes.
Preheat oven to 425 degrees.
Cut tortillas into wedges. Place on sheet tray and toss with olive oil and salt. Bake for 9 to 12 minutes until crispy, tossing several times while cooking. Remove from oven.
Remove about 1 cup of sauce from skillet. Place a layer of tortillas into sauce, add the black beans, sprinkle with cheese, add more sauce and tortilla chips and top with cheese. Place back into oven for 10 minutes.
In a nonstick skillet, fry eggs until sunny side up. Set aside.
Remove chilaquiles from oven and top with red onion, cotija cheese, cilantro and fried eggs. Sprinkle with salt and pepper.