Baked Ranchero Eggs with Blistered Pepper Jack Cheese

For the sauce: 

jalapeño pepper, seeded and chopped

(1 28 oz. can) whole tomatoes, fire-roasted preferred

medium yellow onion, roughly chopped

garlic, peeled and crushed

Salt and pepper,

(1 15 oz. can) black beans, drained and rinsed

For the tortilla strips: 

olive oil, divided

small (6-inch) corn tortillas, cut into ½-inch wide strips

Coarse salt,

large eggs

coarsely shredded pepper jack cheese*

greek yogurt or sour cream (low fat is fine)

freshly squeezed lime juice

minced fresh cilantro