Coat the bottom of a skillet with a little vegetable oil. Heat on high heat. Place the tomatillos in the pan and sear on one side, then flip over and brown on the other side. Remove from heat.
Place the cooked tomatillos, onions, cilantro, lime juice, and jalapeno in a blender or food processor and pulse until all ingredients are coarsely chopped and mixed.
Crack eggs in a bowl and whisk. Add oil to skillet that cooked tomatillos then add eggs. Move periodically with wooden spoon or spatula until consistency you like is achieved.