Preheat the oven to 375°F (190°C) and lightly coat a 9x13 inch baking dish with non-stick spray.
Boil the chickpea pasta in salted water for 2 minutes less than the package instructions for al dente. Drain and set aside.
Heat olive oil in a large skillet over medium-high heat. Add chicken cubes and sauté until golden brown and cooked to an internal temperature of 165°F (74°C). Remove from heat.
In a large mixing bowl, whisk together the Greek yogurt, skim milk, minced garlic, Italian seasoning, salt, pepper, and 0.75 cups of the grated Parmesan cheese until a smooth emulsion forms.
Incorporate the cooked pasta, cooked chicken, and fresh baby spinach into the yogurt mixture, folding gently until all components are evenly coated.
Transfer the mixture into the prepared baking dish, spreading it into an even layer.
Distribute the shredded mozzarella and the remaining 0.25 cups of Parmesan cheese uniformly over the top.
Bake for 20 to 25 minutes until the cheese is melted and the sauce is bubbling at the edges.
Allow the dish to rest for 5 minutes before portioning to ensure the yogurt-based sauce sets properly.