Add everything but the pecans to a saucepan over medium heat and stir well, heating for 1 min. Add the pecans and stir well, then let cook for 3-5 minutes over medium heat, stirring often, until the glaze thickens and cooks down - it should look shiny and should be thick (if it's not, they will not set).
Transfer to parchment paper to cool completely before breaking up.
Using the shredder attachment on your food processor, a mandoline, a knife, shred your brussels sprouts into 1/16” shreds. You can also buy a bag of pre-shredded brussels sprouts at most grocery stores.
Combine the brussels sprouts, pomegranate, apple, pecans, cranberries and parmesan in a bowl. Whisk together all of the dressing ingredients, pour over the salad, and toss.
Let the salad sit for about 30 minutes before serving. As it sits, the acid in the dressing will soften up the sprouts. Serve with extra parmesan, pomegranate, and pecans.
