First of all, the example you provided is not incredibly inefficient; its only slightly inefficient; its inefficiency is below the perceptible level. But, in any case, let's move on with the question.
The way I understand it, when we speak of separation of UI and Logic, we mean avoidance of close coupling.
Close coupling refers to the situation in which the UI knows (and invokes) the logic, and the logic knows (and invokes) the UI. To avoid close coupling one does not need to resort to abolishing coupling altogether. (That's what you seem to be aiming at by demolishing the interface between them down to a least-common-denominator string interface.) All one needs to do is to employ loose coupling.
Loose coupling means that A knows B, but B does not know A. In other words, the two parties involved play distinct client and server roles, where the client knows the server, but the server does not know the client.
In the case of UI and logic, the best way of arranging this in my opinion is by seeing the logic as a server, and the UI as a client. So, the UI is built for the logic, has knowledge of the logic, and invokes the logic, while the logic knows nothing about the UI, and simply responds to the requests that it receives. (And these requests happen to come from the UI, but the logic does not know that.)
To put it in more practical terms, nowhere within the source code files of the logic should you find any include/import/using statements that refer to UI files, while the source code files of the UI will be full of include/import/using statements that refer to Logic files.
So, to come back to your case, there is absolutely nothing wrong with the fact that the UI code which populates the combo-box knows about the hamburger class. There would be a problem if the hamburger class knew anything about combo boxes.
Incidentally, this design allows another thing which you should expect from such a system: it should be possible to plug as many different UIs as you wish to the logic, and the whole thing should still work.