Preheat oven to 375 degrees F (190 degrees C). Grease a 9-inch square baking dish.
Heat olive oil in a skillet over medium heat; cook and stir ground turkey until crumbly and browned, 5 to 10 minutes. Add butternut squash and onion to ground turkey; cook and stir until squash is slightly tender, 5 to 10 minutes. Drain any excess grease from skillet.
Whisk milk, mozzarella cheese, butter, eggs, salt, and pepper together in a bowl; stir into turkey mixture. Transfer squash-turkey mixture to the prepared baking dish. Sprinkle crackers over squash-turkey mixture.
Bake in the preheated oven until cooked through and bubbling, 25 to 30 minutes.