Bring a large pot of salted water to a boil. Cook the chickpea pasta according to package directions until al dente, usually 7-9 minutes. Before draining, reserve 1/4 cup of the pasta water.

Drain the pasta and immediately rinse under cold running water for about 30 seconds to stop the cooking and cool it down completely. Shake off excess water and transfer to a large mixing bowl.

While the pasta cooks, toast the pine nuts in a dry skillet over medium-low heat for 2-3 minutes, stirring frequently, until golden and fragrant. Watch carefully as they burn quickly. Remove from heat and set aside.

Add the pesto and olive oil to the cooled pasta. Toss well to coat every piece. If the mixture seems dry or the pesto isn't coating evenly, add 1-2 tablespoons of the reserved pasta water and toss again.

Add the halved cherry tomatoes, mozzarella pearls, and balsamic glaze to the pasta. Gently fold everything together until well combined. Season with salt and pepper to taste.

Transfer to a serving bowl or platter. Top with toasted pine nuts and torn fresh basil. Drizzle with additional balsamic glaze for presentation. Serve immediately or refrigerate until ready to serve.