For all the lunches and dinners where you truly don’t want to know the answer to the question “what would you like to eat?,” there is this: a chopped cheese. A staple of New York bodegas, it’s something like a burger as a sandwich: same ingredients, different presentation. You wouldn’t be wrong in comparing it to a Philly cheesesteak, albeit with burger flavors.
Assuming your roll isn’t overly crusty or bready, a toddler comfortable holding, say, a quarter or half of a burger should have no issues holding and nibbling from his/her half without having to cut it further. If further cuts are needed, be sure and really smash down the sandwich before cutting so contents don’t spill out. Serve with condiments on the side, for dipping.
When you think about it, this is really just a mayo-slicked grilled cheese sandwich on a different kind of bread. So if your kiddo isn’t in love with the delivery mechanism, or just really likes grilled cheese, just do the following: make the meat-cheese mix as described; mayo or butter up two slices of sandwich bread; toss the meat into between the bread and place in a panini and waffle maker until crisp.