Cut peppers in half leaving the stem on. Grill cut side down for about 7-10 minutes until they begin to soften and are slightly charred. Remove from grill and drizzle the insides with a small amount of olive oil. Salt and pepper the insides, not too much salt as the feta is salty. Sprinkle with the fresh oregano reserving some for the top. Divide the cheese among the peppers. Crack one egg into each pepper. Grill again but on indirect heat for 12-15 min. or until the whites are set and the yolks remain runny. Place a lid over them if cooking on a open fire. Salt and pepper the eggs and top with the remaining oregano. Serve immediately.