Preheat the oven to 450˚F and place the oven rack in the middle position. Line a large baking sheet with foil and set aside.
Trim the stems of the Brussels sprouts and peel away the outer leaves. Using the food processor with the slicing attachment, shave the Brussels sprouts 3-5 at a time until they are all sliced into a slaw.
In a large mixing bowl, toss the shaved sprouts with olive oil. Spread them out on the prepared baking sheet and sprinkle generously with salt and pepper (I use around ½ teaspoon salt and ¼ teaspoon of pepper)
Roast the Brussels sprouts in your preheated oven for 15-20 minutes, turning halfway through. Once the edges have browned all the way across the top, it's time to turn, then duplicate the timing for the other side.
While the sprouts cook, get your dressing made: heat the oil over medium heat until melted and shimmering. Add the shallot and garlic and sauce around a minute until they are fragrant.
Add the remaining dressing ingredients (orange juice, honey, and vinegar) to the pan and simmer for around 5 minutes or until slightly thickened.
When the sprouts have finished cooking, remove the oven to a large serving bowl and toss with the cranberries and dressing. Top with walnuts and serve warm.
If you're wanting to eliminate any added sugars, consider adding a little zest from the orange and a touch more orange juice instead of honey and look for unsweetened dried cranberries like these.