For the authentic texture, do not just shred the cabbage. Use a food processor to pulse the cabbage and carrots until they are roughly the size of rice grains. This increased surface area allows the dressing to coat every piece.
Grate the onion into a large bowl. This releases the juices, which will mix directly into the dressing rather than leaving sharp, crunchy bits of raw onion.
In a separate medium bowl, whisk the sugar, milk, buttermilk, and both vinegars until the sugar is completely dissolved. Slowly whisk in the mayonnaise and lemon juice until the mixture is glossy and smooth.
Stir in the salt, pepper, and celery salt. Taste the dressing; it should be quite sweet and tangy at this stage, as the cabbage will eventually dilute it slightly.
Pour the dressing over the minced cabbage and carrots. Toss thoroughly with a large rubber spatula until every grain of vegetable is submerged.
Cover the bowl tightly and refrigerate for at least 4 hours, though overnight is best. This is not just for chilling; the acids in the dressing actually "cook" the cabbage slightly, softening the crunch into that specific tender texture.
Before serving, give the slaw a vigorous stir. The dressing will have thinned slightly as the cabbage released its moisture, creating the classic "soupy" consistency.