Wash the sprouts in a colander. Cut off the tough ends of the sprouts and any browning outer leaves. Then slice the sprouts lengthwise as thinly as possible using a sharp chef’s knife. Give them a few extra chops for good measure. You may also shred the Brussels sprouts in a food processor, using the slicing blade.
Toast the raw, slivered almonds in a dry pan over medium heat for three to four minutes, stirring frequently, until they are fragrant and turning golden on the edges.
Mix the dressing ingredients - olive oil, vinegar, honey, mustard and garlic - in a covered glass jar. Shake well.
In a medium serving bowl, toss the shredded Brussels sprouts with the almonds, dried cranberries and Parmesan cheese. Add the honey mustard dressing and toss again. Taste and adjust as needed. Serve immediately, or cover and refrigerate for up for 4 days.