Use the grater disk to shred the broccoli in a food processor - use the stems and the blossoms.
In a large bowl, combine the shredded broccoli, carrots, red onion, and cranberries.
In a small bowl, whisk together the mayonnaise, lemon juice, vinegar, sugar, salt, and a generous quantity of fresh pepper. Add the dressing to the broccoli mixture and toss to combine. Taste and add more salt or pepper, if needed.
Allow to sit for 30 minutes (or an hour in the fridge) so the flavors can mingle. Right before serving mix in the sliced almonds.