Set in a late-night diner, the poem treats appetite as something bigger than food. The opening lines are blunt and a little comic: someone eats a sandwich "beyond all shame," then moves on to a stew. Hunger here has no manners and no limit.
Then the tone shifts. The claim that "some of the best parts of joy / are contrary to faith" suggests the speaker sees pleasure and religious restraint pulling against each other. Eating, and maybe desire in general, feels like the joy that doesn't fit the rules. The "infinite mouth" could be the speaker's own craving, or human wanting in general, and the question "what will be the end of it" sounds half amazed, half worried.
The last two lines bring in the Last Supper, which suggests the poem is playing with religious imagery. The speaker wishes there were no final meal, meaning no end to the feasting. The mood is wry and hungry, with a quiet fear of endings under the jokes.