Definitely.  That’s where the traditional egg in a hole is made.  You’ll want to prep the bagels the same way as for the baked egg in a hole. Instead of putting the cut side down onto a baking sheet, you’ll put butter in the pan over medium high heat, and put the bagel in the pan with the cut side down and then crack the egg into the middle.  Let the egg set, then flip and let cook until it’s done to your specific taste.  This makes a great work at home lunch option. Top the bagel egg in a hole with lox, red onion and spinach for a gourmet experience!