First zest the orange. This will be easier to do when the orange isn't cut, so just make sure you zest only the half you're using. Take out a microplane or other zester, as well as a medium bowl. If using a microplane, place it against the rim of the bowl. Zest the orange by rubbing it against the microplane in short swipes, scraping just the vibrant orange skin off into the bowl and not the lighter pith underneath. You may need to wipe the zest off the bottom of the microplane with your finger to get it all off.
Once the zest is off, use a sharp knife and cutting board to cut the orange in half, then if necessary cut the half you're using into quarters, depending on what type of juicer you're using. Juice the orange into the same bowl as the zest, discarding the used parts of the orange.
Take out a 16 ounce mason jar and measuring spoons and add the apple cider vinegar, oil, kosher salt, and dijon mustard into it. If your honey is very fluid go ahead and add it to the jar as well. If not, put it in a small microwavable bowl and warm it for about 10 seconds, then add it into the mason jar.
Pour the juice and zest into the jar, add the lid, then shake vigorously to combine all of the ingredients together. Set aside while you make the slaw.
Using the same knife and cutting board, thinly slice the cabbage. If you're starting with a small whole head, cut it in half, otherwise start with the half you have. Cut out the thick internal stem in the bottom middle of the cabbage by making two deep cuts along the edges of the stem into the cabbage. Angle the cuts as best you can so they point into the cabbage and not straight back. The resulting piece you cut out should be triangular in shape (see the pictures in the above blog post). You may have to make several cuts to get the internal stem all out.
Next cut the cabbage half in half again (so you have a quarter of a cabbage). Set one of the quarters aside and lay the other quarter on the cutting board with one flat side down. Start making small slices with your knife on the other flat side of the cabbage, cutting as thin as you like and are able to with the knife. Keep slicing until all of the cabbage is cut, then put the sliced cabbage into a large bowl. Do the same with the other cabbage quarter.
Add the shredded carrots to the bowl with the cabbage as well. Take the jar of dressing out and give it a shake to make sure the ingredients are combined, then pour the dressing over the carrots and cabbage. Use a pair of kitchen tongs to stir everything together, coating the veggies with the dressing.
Take a bite of the slaw and see if it needs more salt. I typically like to add anywhere between ¼ and ½ tsp more kosher salt to it. Stir again with the tongs to combine. The slaw can be served right away, though does taste better the next day (when the cabbage has softened and the flavors have melded) after being stored in an airtight container in the fridge.