With the skillet set at 375F, sweat onion for 5 mins. Then add poblano, jalapeno, and garlic and cook for another 5 mins. Add cumin, hearty pinch of cayenne, and ½ cup cilantro stems. Add the green tomatoes and cook for another 3 mins, then add chicken stock. Then sprinkle feta around the skillet and add salt. Let cook for 3 mins.
Now, to get the eggs we need, we need to remove about 2/3 of the egg whites. This will help the eggs cook to a nice custard-like texture. Gather four small ramekins, and set nearby. To remove egg whites, gently crack the egg and cup the egg yolk back and forth between the halves, until some of the whites are removed. Add the egg yolks to the ramekins, with two yolks in each. Once separated, add egg yolks (in their pairs) to their own separate spaces in the electric skillet. Lower to 300 F, cover and cook for 10 mins. Once the yolks are beginning to custard, and the bit of remaining egg whites are beginning to set, turn off skillet.
Garnish with cilantro leaves and serve in small bowls, giving each bowl its pair of cooked eggs.