Preheat oven to 400°F and line a large baking sheet with parchment paper.
Rinse and drain the chickpeas, then pat them thoroughly dry with a paper towel to ensure they become crisp during roasting.
In a large mixing bowl, toss the dried chickpeas, broccoli florets, and chopped red bell pepper with the olive oil, smoked paprika, garlic powder, sea salt, and black pepper until evenly coated.
Spread the mixture in a single layer on the prepared baking sheet, ensuring enough space for air to circulate.
Roast for 20 to 25 minutes, tossing the ingredients halfway through, until the chickpeas are golden and the vegetables are tender with charred edges.
While the vegetables roast, whisk together the plain Greek yogurt and lemon juice in a small bowl until the consistency is smooth and creamy.
To serve, spread the lemon-yogurt mixture across the bottom of a wide bowl and pile the warm roasted chickpeas and vegetables on top.