> There is an old trope of counting sheep to fall asleep, but that's not a dream.
How about when people dream about what they were thinking about when they fell asleep? It happens.
In the context of the story, i think "dream" should be taken as "yearn for" i.e. something you dream of having one day, not so much what you dream of at night.
Those meanings are connected. I think it was a reference to counting sheep but it describes yearning as far as connecting the title to the plot.
Also, upon further reflection I don't really agree with what the other commenter said: "There is an old trope of counting sheep to fall asleep, but that's not a dream". If you try to and manage to think in a way that causes you to become less alert, it starts to be like daydreaming, so I think this sort of falling asleep thinking is under the umbrella of dreaming.