8 1⁄2-inch-thick slices sourdough bread or rye miche
5 garlic cloves, halved
10 medium fresh tomatillos, husked, or 1 (13 oz) can tomatillos, drained
1 cup roughly chopped cilantro
1 jalapeño, seeded
1 cup chopped white onions
1⁄2 tsp salt
1⁄2 tsp freshly ground black pepper
1 (15 oz) can black beans, drained and rinsed
1 ripe avocado, pitted and peeled
2 tbsp freshly squeezed lime juice
8 large eggs
1⁄4 cup crème fraîche
Rub bread well with garlic; reserve remaining garlic. Heat a large skillet over medium heat, add oil, and pan-toast bread.
To make the tomatillo sauce, boil tomatillos in salted water until soft, about 10 minutes. (For canned tomatillos, skip boiling.) In a blender, puree tomatillos, reserved garlic, 3⁄4 cup of cilantro, jalapeño, onions, salt, and pepper until smooth. Add a little water (about 1/3 cup) to thin mixture. Set aside.
In a medium bowl, mash black beans, avocado, and lime juice, leaving mixture a little chunky. Spread 1/3 cup on each toast and set aside.
Heat tomatillo sauce in a large pan over high heat. When hot, crack 2 to 3 eggs into sauce and cook until whites are opaque but yolks are still runny, about 4 minutes. Season to taste with salt and pepper. Remove each with a slotted spoon and place it on toast. Repeat with remaining eggs.
Let sauce thicken slightly, about 5 minutes. Remove from heat, stir in crème fraîche, and pour about 1⁄4 cup over each toast slice. Garnish with remaining cilantro and black pepper.