Preheat your oven to 400°F.

Toss the Brussels sprouts with 2 tablespoons of the oil on a large baking sheet. Season with salt and pepper and roast until golden and crisp, 20 to 25 minutes, stirring about halfway through.

Meanwhile, whisk together the tahini, lemon zest and juice, garlic, Dijon, and vinegar. Add 2 tablespoons of water, the extra virgin olive oil, ½ teaspoon pepper, and salt to taste. Whisk until well combined and set aside.

Heat the remaining 1 tablespoon of oil in a small skillet set over medium-high heat. Drain the capers well and dry them off on paper towel. Add the capers to the skillet and fry until crisp, about 1 minute, being careful of splatter. Using a slotted spoon, transfer the capers to paper towel to drain.

When the Brussels sprouts are roasted, spread the Caesar dressing over a serving dish and top with the sprouts. Scatter the capers, almonds, Parmigiano-Reggiano, and a little more pepper, if desired, over top.