Preheat your oven to 425F and line a baking sheet with parchment. Place the broccoli on the baking sheet and spray it with oil, or drizzle it with oil and use your hands to coat everything evenly. Season the broccoli with salt and pepper.
Next, prepare your bread. If you'd like to use fresh bread crumbs, add the bread cubes to your food processor and process until they're coarsely ground (these should be bigger, rustic bread crumbs, not too finely ground). It should take about 30-45 seconds. Add these crumbs to another parchment lined baking sheet. If you'd like to skip the food processor and make croutons, simply add the cubed bread to another lined baking sheet.
Transfer the broccoli and the bread to the oven. Toast bread crumbs or croutons for five minutes, stir, and then toast for another 3-5 minutes, or until browning and crispy. Remove the bread from the oven. Roast the broccoli for 25 minutes, or until the stems are tender and the broccoli is browning and crispy.
While the broccoli roasts, prepare the dressing. Combine all ingredients in a high-speed blender or food processor till smooth. You should have around 1 1/2 cups dressing, and you'll use 3/4-1 cup for the recipe. Save extra for other salads or for bowls, or freeze it for up to 6 weeks.
Add the romaine to a large mixing bowl, along with the capers, parmesan, crumbs or croutons, and nori or dulse, if using. Add 3/4 cup dressing and toss well to combine. Fold in the broccoli, then add more dressing as needed until everything is coated well. Serve, with an extra sprinkle of vegan parmesan if you like.