Make the beans: Heat the olive oil in a large skillet over medium-high heat. Add the yellow onion and cook until almost translucent, about 4 minutes. Add the garlic and cook until softened, about 1 minute. Stir in the chili powder and cumin until combined. Add the green chiles, beans, 1/2 cup water and 1/2 teaspoon each salt and pepper. Bring to a simmer, then reduce the heat to medium low and cook, stirring occasionally, until most of the liquid has evaporated, about 8 minutes; set aside.
Meanwhile, make the pickled red onion: Combine the red onion, vinegar and 1/4 cup water in a small bowl. Let stand until bright pink and slightly softened, 10 to 15 minutes; drain.
Make the crema: Combine the yogurt, lime juice, cayenne, 4 teaspoons water and 1/2 teaspoon salt in a small bowl.
Arrange the cucumber, jicama, radishes and lettuce on a platter. Top with the bean mixture, crema, avocado, jalapeños, pickled red onion, cilantro and cheese.