Strictly speaking, this is a structure known in linguistics as "middle voice" (although you don't often see that term used when talking about English grammar). In many languages it's explicitly marked, but in English it usually takes the form of a verb that looks like it's active voice but has passive meaning.
As other people have already said, "the dessert eats well" is grammatical, although for many people sounds a little bit forced. There are, however, plenty of other examples of the middle voice in English where it's alive and well. A simple example:
Active voice: "The ball broke the window" (the ball is subject and is causing the action of breaking)
Passive voice: "The window was broken by the ball"
Middle voice: "The window broke" (the window is subject, but underwent the action of breaking)
Active voice: "The sun melted the ice" (the sun is subject and causing the action of melting)
Passive voice: "The ice was melted by the sun"
Middle voice: "The ice melted" (the ice is subject, but underwent the action of melting)
In each case, the middle voice form is derived from a transitive active voice verb, but with the object of the transitive form being used as the subject of the intransitive middle voice form.