Preheat the broiler to high and line a baking sheet with foil; spray the foil lightly with cooking spray.
In a bowl, toss the chicken tenderloins with the yogurt and 1/2 teaspoon of the garam masala until evenly coated.
Arrange the chicken on the prepared sheet, sprinkle with 1/4 teaspoon salt, and broil on the top rack 2–3 minutes per side until cooked through; remove and let rest.
While the chicken cooks, heat the olive oil in a nonstick skillet over medium-high heat and sauté the sliced squash about 2 minutes.
Add the remaining 1 1/2 teaspoons garam masala, grated ginger, ground red pepper, ground coriander, and minced garlic; cook 1 minute until fragrant.
Stir in the diced tomatoes and simmer about 4 minutes until much of the liquid evaporates, then stir in 2 tablespoons heavy cream and 1/2 teaspoon salt and cook 1 more minute.
Cut the cooked chicken into bite-size pieces and add to the skillet; toss to coat with the sauce.
Place the naan on a baking sheet and broil 1 minute per side to warm and lightly char.
Divide the chicken mixture evenly among the warm naan rounds, top each with sliced mozzarella and red onion, then broil 2 minutes until the cheese melts.
Sprinkle with fresh cilantro leaves and serve immediately.