1. Add the chicken, salsa and hot sauce to a medium saucepot with a lid. Place over low heat to warm through.
2. Melt 2 tablespoons butter with the oil in a large nonstick skillet over medium-high heat. Once the butter melts, add half the corn tortillas, increase the heat to high and fry the tortillas, stirring constantly, until crisp and golden brown, 3 to 4 minutes. Once crisp, pour the chips onto a paper-towel-lined baking sheet and generously season with salt. Add 1 more tablespoon butter to the skillet and repeat with the remaining tortillas.
3. Wipe out the nonstick skillet and melt the remaining 2 tablespoons butter over medium-high heat. Once the butter is melted, gently crack the eggs into the skillet. Once the whites are just beginning to set and turn white, partially cover the skillet with the lid and let the eggs cook through, 1 or 2 minutes for sunny-side up.
4. To build your chilaquiles, plate a generous pile of fried tortillas and top with the tomatillo smothered shredded chicken. Drizzle over some crema, sprinkle some cilantro leaves and white onion, crumble some cheese over top and finally top it all with a beautifully fried egg. Serve with lime wedges and additional hot sauce on the side.