From a recent scanned sefer at JNUL. (You need a plugin to view the sefer, and then look at the top of page 66.) It is a sefer full of sermons for moadim, including for Rosh HaShanah. And at the end, the author includes this zemer. There are actually more stanzas, but I am just including the beginning. The title is:
זמר לסעודת כל יום בין ברכת המוציא בין האילת כת
or something like that. I am actually not certain about the last two words.
My first guess is that the printer messed up these letters and it really reads האכילת פת, by leaving out a kaf in the first word. But this would be astounding -- a zemer between HaMotzi and the eating? Then again, there is an established halachic position that after the botzeia eats, everyone else can talk even before eating their bread. (Note: Don't pasken or act based on blogs.) If so, this zemer would be appropriate for this time. Or perhaps (!) they would not consider saying this zemer, about Hashem providing food, to be a hefsek.
An alternative is that the last two words are HaAyelet Koach, where Ayelet Koach is some known zemer, and so they are saying that this zemer of the author's creation should precede that in the course of the meal, and should follow Birkat HaMotzi and of course eating of the bread.
Or perhaps the words say something else. Any suggestions? Thanks in advance.