Preheat the oven to 400 degrees. Trim and scrub beets. Brush each beet with a drizzle of olive oil and wrap in aluminum foil. Roast beets on the center rack of the oven for 45 to 60 minutes, until tender. Remove from oven, open foil and let cool.
While the beets are roasting, prepare the dressing and other ingredients. You can use pre-shredded cabbage (recommended) or use a mandoline or very sharp knife to slice a head of red cabbage. For the dressing, combine the shallot, mustard, and vinegar in a small bowl or dressing jar, and let this mixture sit for ~15 minutes. Then add the olive oil and whisk/shake until well combined.
In a large bowl, combine the shredded cabbage and dried cranberries. Using a hand grater, shred the apple and cooked beets into the bowl. Add the vinaigrette and mix until combined.
You can serve immediately, or put this in the fridge for 30 minutes to an hour, and serve cold. Just before serving, squeeze the lemon on top of the slaw and stir. Enjoy!
Look for Love Beets or a similar brand at the store if you want to use pre-roasted beets.
Leftovers can be stored in an airtight container in the fridge for up to 4 days. You can also freeze this slaw in an airtight container or plastic bags for up to 3 months. Thaw in the fridge.
This slaw can be made up to a day in advance, with or without the dressing. If you are nervous about it getting soggy, wait to add the dressing 30-60 minutes before you serve it.