Preheat the oven to 375 degrees F. Toss the torn sourdough bread with olive oil, kosher salt, and black pepper on a baking sheet. Spread into a single layer and toast until golden brown, about 12-15 minutes, flipping halfway through.

In a small bowl, whisk together the lemon juice, tahini, Dijon mustard, minced garlic, chopped capers, kosher salt, black pepper, and olive oil until fully combined.

In a large bowl, combine the shredded brussels sprouts, chopped parsley, sliced scallions, grated Parmesan, and croutons. Drizzle the dressing over the salad and toss to combine. Top with additional Parmesan upon serving.