Use a knife to widen the hole in two bagels. Just make each hole a little wider to accommodate the eggs. Then slice each bagel in half.
Add butter to a large skillet over medium low heat. Once butter is melted, add bagels, cut-side down. Crack eggs in the middle of each bagel half. Don't worry if some egg spills over the side of the bagels, just try to keep the yolk in the center. Cook eggs and bagels for 2 to 3 minutes on that side until the egg is completely set on the bottom and the bagel is browned.
Use a spatula to carefully flip the bagel. Cook for 45 to 60 seconds on the second side depending on how you like your egg. 45 seconds should give you an over medium egg.
Remove the bagels from the skillet and plate. Season with a pinch of salt and pepper and fresh scallions.