Start by preheating your oven and preparing the croutons. Toss the torn sourdough with olive oil, salt, and pepper. Spread it evenly on a baking sheet so each piece can crisp properly. Bake until golden and crunchy, stirring once for even browning.
In a bowl, whisk together lemon juice, tahini, Dijon mustard, garlic, capers, salt, pepper, and olive oil. Keep whisking until the mixture becomes smooth and creamy. Taste and adjust seasoning if needed. The dressing should be tangy, rich, and balanced.
Place the shredded Brussels sprouts in a large bowl. Add parsley, scallions, Parmesan, and cooled croutons. Pour the dressing over the top and toss everything together until evenly coated. Sprinkle extra Parmesan before serving for added flavor and presentation.