First, cut your cabbage in half, then into quarters. Cut out the hard core from each piece. Using a mandoline or sharp knife, shred the cabbage into thin strips. Don't make them too thick or too thin - aim for about 1/8 inch wide. Put all the shredded cabbage in a big mixing bowl.
Peel your carrot and shred it using a box grater. Use the side with the bigger holes for nice, chunky pieces. Add the shredded carrot to the bowl with the cabbage.
Peel and slice the red onion as thin as you can. I use a sharp knife and try to make them paper-thin. To make the taste milder, I soak my onion slices in a bowl of cold water for about 10 minutes. This takes away some of the sharp bite. Drain the onions well and add them to the cabbage and carrot.
In another bowl, mix together the mayonnaise, evaporated milk, lemon juice, sugar, salt, and pepper. Whisk everything together until it's smooth and creamy. Taste it and adjust - if you want it sweeter, add more sugar. If you want it tangier, add more lemon juice.
Pour the dressing over the cabbage mix. Use a big spoon to toss everything together until all the veggies are coated nicely. Make sure every piece gets some dressing on it.
I like to let my coleslaw sit in the fridge for at least 30 minutes before serving. This lets the flavors come together and the cabbage softens just a little. Give it a quick stir before you serve it.