Blessing on Food Not Intended to Eat at the Time of the Blessing

I am on a diet and took half a slice of cake, intending to eat only that and nothing more. After finishing, I wanted to eat another half slice (and that's it for now). Do I need to recite the first blessing again?

Indeed, you need to recite the blessing again. (Especially since you are on a diet, and therefore, you had a clear intention not to eat another half slice)

It is written in the Shulchan Aruch, Orach Chaim, Siman 206, Seif 5: "One does not bless on food or drink until it is brought before him; if he blessed and then it was brought before him, he must bless again; but if one blessed on fruits before him and then more of the same kind or another kind with the same blessing was brought, he does not need to bless again." And the Rema wrote: "It is good to initially intend for everything that will be brought to him." Later authorities disagreed on the Shulchan Aruch's ruling when one did not intend to exempt and ate without intention, of the same kind. And the Mishnah Berurah ruled that if he ate without intention, he does not bless again on the same kind (and not when the blessing is the same as the first). And these are his words in S"K 20: "Even if he did not explicitly intend for everything that would be brought to him, but blessed on these fruits that were before him without intention, we say that it is as if he explicitly stipulated that if more is brought to him, he will eat from them as well. Because it is the way of a person to move from small to large. Unless he explicitly intended not to eat except for those fruits before him, or when he finished eating he decided not to eat more, and then changed his mind to eat, in this case, all agree he must bless again." And so it is written in Shaar HaTzion, Siman 168, S"K 21.