Have you heard of these? I've never seen them outside of New England, but when we lived in Boston, every dinner had grilled bagels on the breakfast menu. Yes, this bagel's hole closed-up. Thanks for noticing. These are the sourdough bagels from the other day that are now gone save for one which will no doubt end up grilled in the morning. Here's how you do it:
In a heavy frying pan, melt over medium heat a good tablespoon and a half of butter. Place the bagel half cut side down. Weight the bagels with a heavy pot on top. If you don't have one, that's OK-just press well with a spatula.
And that's pretty much it. Fry them until the butter forms a lovely crust. In Boston, people actually add cream cheese in addition to all that butter. Do as you see fit.