Remove any wilted or damaged outer leaves from the cabbage and rinse the cabbage and carrots, then pat them dry. Set the cabbage on a stable cutting board with a damp towel underneath it. Trim the stem end just enough to make a flat base, cut the cabbage in half from top to bottom, and then cut each half into quarters. On each quarter, make two angled cuts around the hard white core and discard the core. Place each wedge flat side down and use a sharp chef's knife to slice crosswise into very thin ribbons, about 1/8 inch wide. For shorter, easier to eat pieces, cut the longest ribbons in half. Peel the carrots, trim off both ends, and grate them on the large holes of a box grater, using long downward strokes; stop when the remaining piece is too small to hold safely. A food processor fitted with a slicing disk for the cabbage and a shredding disk for the carrots may be used instead. Put all of the shredded cabbage and carrots in a large bowl and toss to combine.

In a small bowl, whisk together the apple cider vinegar, sugar, Dijon mustard, celery seeds, kosher salt, and black pepper. Continue whisking for 1 to 2 minutes, scraping the bottom of the bowl, until the sugar and salt are mostly dissolved and the mixture no longer feels gritty. Slowly whisk in the vegetable oil until the dressing is evenly blended.

Pour the dressing evenly over the cabbage and carrots. Using tongs or two large spoons, lift and turn the vegetables from the bottom of the bowl until every piece is lightly coated. Cover the bowl and refrigerate for 8 hours so the vegetables can soften slightly and absorb the dressing. Toss the slaw again before serving; taste and adjust with a small pinch of salt or pepper if needed. Serve chilled, using a slotted spoon if extra dressing has collected at the bottom.