Place squash halves, cut-side down, in a microwave-safe dish. Add 2 tablespoons water. Microwave on High until the squash is tender, about 10 minutes. (Alternatively, place squash halves, cut-side down, on a rimmed baking sheet. Bake in a 400°F oven until the squash is tender, 40 to 50 minutes.) When cool enough to handle, use a fork to scrape the squash flesh from the shells into a medium bowl. Place the squash shells, cut-side up, on a rimmed baking sheet.
Heat oil in a large skillet over medium-high heat. Add chicken, broccoli and salt; cook, stirring, until the chicken is cooked through and the broccoli is tender, about 5 minutes. Add garlic and cook, stirring, for 1 minute.
Whisk milk, Parmesan, cornstarch and pepper together in a measuring cup. Add to the pan and cook, stirring, until thickened, 1 to 2 minutes more. Stir in the squash flesh. Fill the squash shells with the chicken mixture. Top with mozzarella. Bake until heated through and cheese has melted, 12 to 15 minutes.
435 calories;22 g fat(9 g sat); 5 g fiber; 28 g carbohydrates; 34 g protein; 69 mcg folate; 87 mg cholesterol; 10 g sugars; 0 g added sugars; 2,351 IU vitamin A; 59 mg vitamin C; 385 mg calcium; 2 mg iron; 702 mg sodium; 860 mg potassium
Vitamin C (98% daily value), Vitamin A (47% dv), Calcium (38% dv)