Preheat the oven to 425°F (220°C). Line a large rimmed baking sheet or leave unlined if preferred.
Place the broccoli florets and rinsed, drained chickpeas on the baking sheet. Drizzle with 2 tablespoons olive oil and toss to coat. Season with kosher salt and black pepper to taste.
Roast the broccoli and chickpeas for 15 to 20 minutes, until the broccoli is tender and the chickpeas are crisp, stirring once halfway through.
While the vegetables roast, heat 1 tablespoon olive oil in a small skillet over medium heat. Add the panko, 1/2 teaspoon garlic powder, and a pinch of salt. Cook, stirring frequently, until golden and toasted, about 2–3 minutes. Transfer to a plate to cool.
Make the dressing by whisking together the tahini, Greek yogurt, lemon juice, Dijon mustard, minced garlic, anchovy paste, 1 tablespoon grated Parmesan, and 2 tablespoons water. Season with kosher salt and black pepper to taste. Add more water, 1 teaspoon at a time, if the dressing is too thick.
Assemble the salad by placing the roasted broccoli and chickpeas in a serving bowl. Drizzle the tahini-Caesar dressing over the mixture and toss until evenly coated.
Top with the toasted panko, 1/4 cup freshly grated Parmesan, and a sprinkle of crushed red pepper flakes. Serve immediately.