Yvo of Feisty Foodie was initially annoyed when her Ultimate Stuffed Burger ($10.99 with fries or salad, and soda) from Burger Burger in the Financial District appeared to be missing barbecue sauce and cheddar cheese, but as she ate it she realized the cheese and barbecue sauce were stuffed inside the patty, along with bacon. Although she gave the burger a thumbs up, she took issue with the burger's doneness and its impact on the cheesy filling:
The inside was medium rare, but this meant the cheese didn't melt and instead I had little cubes of cheese in my mouth and sandwich that would have been that much better had they been melted, oozing into the patty and each other. So it would probably have been best to skip asking me how I want my burger and in the case of the stuffed one, just serve it properly cooked.
This is related to the reason I don't like stuffed burgers: I prefer my burgers medium rare, but in a stuffed burger that would result in non-gooey cheese filling. However, to get gooey cheese the meat has to be cooked past medium rare. I suppose with a stuffed burger it's better to go with the overcooked meat than cubes of cheese.
Cheese-Stuffed Burgers from the Stumble Inn in New York City
The Stuffed Cheeseburger at the Iron Horse in Westwood, New Jersey, and the Failbun
Good Dog's Cheese-Stuffed Burger in Philadelphia