There are a hundred different names for an egg in toast, but I've only ever seen one Eggs Rothko ($9). It's hardly a new discovery; it's the sort of dish I have so often and recommend so often I was surprised to find we'd never written about it.
If you've never had the pleasure of meeting the Rothko, served at Egg in Williamsburg, Brooklyn, here you go: it's a thick, thick slice of brioche (from Amy's Bread) with an egg cooked in the middle, and all of that's covered in a blanket of melty Grafton cheddar. The delicious cheesey oils meet the already buttered bread so that no bit of brioche is untouched; it's got all the merits of a grilled cheese, plus the added bonus of a runny egg. It comes with tomatoes and one side of meat: pictured here is excellent country ham (from Col. Bill Newsom's), though I find the scrapple even better. Lots of food for nine dollars, especially when you include the eggy, fryer-fresh beignets that come out before every brunch entree.
For those not inclined toward that much cheese in the morning, consider the chorizo ($12), an impressive pile of their housemade loose sausage with toast and two eggs any style. It's spicy and vinegary and crisped up so that each little clump has a crusty edge, and its oils tend to run off and coat the eggs in a very, very good way.