Cuban-like --I like it. It might describe me. Que culpa tengo yo, de no haber nacido en Cuba?
Latin America, and much of the world, has coopted the sanuiche mixto of Cuba (even more so, the medianoche).
There are rules, though, regarding the real thing. Sort of like a Chicago hot dog, certain variations and improvements are great, but basic elements define the sandwich. They are:
Cuban bread, ham, roast pork, Swiss cheese, pickle. Butter is almost always used by Cubans making cubans, almost never by others making Cubans.
Variations include, from almost-orthodox to controvesial:
mustard (or mustard mixed with mayo, very common as a Cuban condiment), Genoa salami, mortadella, lettuce and tomato, bacon, Chicago foodservice white cheese food.
The salami and mortadella are mostly to be found in Tampa, though my father in law, from Havana never stepped foot in Tampa but used mort on his. Lettuce and tomato is something I have never liked on this sandwich, as it throws everything off. It is by all accounts a recent invention. Bacon with lettuce and tomato on top of the traditional ingredients creates the "Miami sandwich" a fitting name for this Cuba-US mix. The easy melting, white processed cheese food used even by Marianao here might have some resonance with Cubans that just left Havana yesterday, since the produce available is dismal, but that is no excuse.
Making a good Cuban at home is pretty easy, especially if you have a press. Even a George Foreman grill works fine. I have a cuisinart griddle/press with a flat surface and a floating hinge that works perfectly for this. The hardest things to find when making a Cuban are the right bread and the lechon. My favorite bread substitute in Chicago is the banh mi form Ba Le. Once pressed, it is getting into the ballpark of the less lardy version of Cuban. As for the pork, make your own. Or shredded carnitas can work, or you can buy lechon from La Unica. Also, Westbrook market sells an Italian roast pork deli meat, porchetta they call it, though it is not, strictly speaking, porchetta. It is the only good version of roast pork I have ever had from a deli. I'm sure you can get it at Caputo's, as that is likely where Westbrook gets theirs. (Boar's Head does/did a Cuban style roast pork that is one of the vilest things you could ever taste.) Westbrook also has the very hard to find Cuban style ham, which is covered in garlic and paprika. I've never been a fan, but it's interesting that they have it.