Preheat the oven to 350 degrees. In a small bowl, combine the cranberries, 1/4 cup hot water and 1 tbsp. sherry vinegar. Let stand until the water is cooled and the cranberries are slightly plumped. [Make ahead: Cover and refrigerate for up to 2 days. Let stand at room temperature for 1 hour before using.]
Spread the walnuts on a parchment-lined baking sheet. Roast, stirring once, until fragrant and lightly browned, about 10 minutes. Transfer to a medium bowl, drizzle with 1 1/2 tsp. EVOO and sprinkle with the sugar; toss well. Let cool. [Make ahead: Seal in an airtight container and store at room temperature for up to 1 day.]
Fill a 6-qt. pot with 3 inches of water and bring to a boil. Add the broccoli; cover and simmer for 5 minutes. Drain in a colander and rinse with cold water until cool. Drain well and pat dry, then coarsely chop. [Make ahead: Transfer to a serving bowl, cover and refrigerate for up to 2 days. Let stand at room temperature for 1 hour before proceeding.]
Pour the cranberries and their juices over the broccoli. Add the remaining 2 tbsp. EVOO and 1 tsp. vinegar; toss well. Season with salt and pepper, then sprinkle the walnuts on top. Serve at room temperature.