In a medium-size bowl, combine grated onion, garlic, vinegar, sugar, salt and pepper. Add chicken and toss to coat well. Cover and set aside to marinate for about an hour.
Pour oil into a large heavy pot to a depth of 1½-inches. Heat to 350° F. Combine flour and cornstarch in a shallow bowl and season with salt and pepper.
Working in batches to avoid crowding, lift chicken from marinade, dredge lightly in seasoned flour and cornstarch, gently drop into oil and fry for 5 to 7 minutes, turning occasionally, until golden brown and crisp. Drain on cooling rack. Repeat with remaining chicken, checking oil temperature between batches.
To assemble, place a couple tablespoons black beans on tostada and spread to cover, then slice avocado and layer on beans, top with Korean chicken; spoon adobo sauce over chicken. Quickly fry an egg over easy in a nonstick pan and place on top of Korean chicken. Drizzle a little crema over egg, garnish with lime and cilantro and extra toasted sesame seeds.
In a large pot, cover the beans with cold water by at least 2 inches. Add oregano and garlic cloves and bring to a boil over high heat.
Reduce heat to simmer and cook until beans are very tender, about 1 to 2 hours. Season with salt. Drain beans, reserving bean-cooking liquid. You should have about 3 cups cooked beans; if more, measure out 3 cups beans and reserve rest for another use. Discard garlic.
In a large sauté pan, heat butter until foaming, over medium-high heat. Add minced onion; cook, stirring occasionally, until translucent and lightly golden, about 7 minutes. Stir in beans and cook for 2 minutes. Add 1 cup reserved bean-cooking liquid. Using fork or potato masher, smash beans to form chunky purée. Reduce heat to medium; cook, stirring, until desired consistency is reached. If refried beans are too dry, add more bean-cooking liquid, 1 tablespoon at a time, as needed. Season with salt.