Heat your broiler to high. Place tomatillos, onion, garlic, and jalapeños on a sheet pan. Drizzle with oil and season with salt and pepper. Broil for 10 minutes, tossing halfway through, until soft and charred. Cool slightly. Remove garlic cloves from their peels.
Add all ingredients to a blender. Blend until smooth, thinning with water 2 Tablespoons at a time until it's your desired consistency. Taste, and season with salt and pepper. Chill the salsa until you're ready to use it.
Preheat the oven to 375° F. In a large saute pan, heat the oil until it's hot and shimmering. Fry the tortillas in 2-3 batches until crisp and golden. Drain on paper towels, and season with salt.
Grease four cocottes (or ramekins). Divide the tortillas between the cocottes, and add 3-4 Tablespoons of salsa verde. Gently toss to coat the tortillas. Make a nest in each cocotte, and crack an egg in the center. Season generously with salt and pepper. Bake for 15-18 minutes, until the whites are set and the yolks are still runny.
Serve the mini chilaquiles verdes with queso fresco, avocado, pico de gallo, cilantro, limes, and/or hot sauce. Enjoy!!