Alliteration is a major feature of "The Emperor of Ice Cream." Its main function overall is to bring out the beauty of everyday things, which helps make the poem's case in favor of the sensuousness of daily life.
Though "big" and "bid" across lines 1 and 2 chime together alliteratively, the first main example is in line 3:
In kitchen cups concupiscent curds.
There's nothing subtle about the alliteration here. It exerts great force on the line, relating to the "muscular" man who comes to make the ice cream. It is deliberately what Stevens would call "gaudy," what modern day readers might think of as tacky and extravagant. It's as though the line takes delight in its own sound, subtly reinforcing the poem's point about the vitality of everyday experience. This alliteration also captures the repetitive work of churning ice cream.
In line 4, "dawdle" and "dress" alliterate to suggest decadence and, in the way that the two words are separated by two intervening words, the slowness of dawdling. These moments, and even the mention of the "boys" who "bring" flowers, all have sexual undertones that are in part aided by the alliterative sound. The poem seems to draw a link between being alive and the possibility of sexual, or "concupiscent," encounters.
In line 9, "dresser of deal" suggests how the poem's interest in beautification applies even to humble objects. This "dresser" is made of "deal," or cheap pine wood, yet even this modest, utilitarian object is shown to be beautiful through the speaker's use of alliteration. The device captures how people's senses give them access to the beauty of ordinary things.
Meanwhile, the /l/ alliteration in line 15 between "let" and "lamp" seems to be more about fixing the line with particular sounds, like an image coming into sharper focus (in this case, the poem's image of a dead woman). Here, alliteration shows how—for all the poem's gaudiness—it is also incredibly precise.