Prick scrubbed sweet potatoes all over with a fork; place on a microwave-safe plate. Microwave on High until tender, 7 to 10 minutes.
Meanwhile, heat 2 tablespoons oil in a large skillet over medium heat. Add 4 cups tomatoes, ½ teaspoon salt and ¼ teaspoon pepper; cook, stirring occasionally, until the tomatoes are softened and release their juices, about 10 minutes.
Stir in 3 teaspoons garlic and ¼ teaspoon smoked paprika; cook, stirring often, until fragrant, about 1 minute. Add rinsed chickpeas; cook, stirring occasionally, until the mixture thickens and becomes jammy and the chickpeas are heated through, about 2 minutes.
In a small bowl, combine ¼ cup yogurt, 1½ tablespoons water and the remaining ¼ teaspoon salt and ½ teaspoon garlic; stir until smooth.
Cut a slit lengthwise down the center of each sweet potato, leaving ends intact. Gently press the ends to open; fluff the flesh with a fork. Top with the chickpea mixture and drizzle with the yogurt sauce. Sprinkle with 2 tablespoons parsley.
