Whisk together 1/2 cup milk and cornstarch in a small bowl until smooth and free of lumps; set aside.

Combine remaining 2 1/2 cups milk with sugar in a medium saucepan over low heat. Slowly whisk in cornstarch mixture. Cook, whisking occasionally, until mixture begins to thicken, 8 to 10 minutes. Add chocolate chips and salt; stir until chocolate is melted and pudding is smooth and thickened, about 7 minutes more.

Pour pudding into 1 large bowl or 6 individual bowls. Place plastic wrap over the top of pudding to prevent skin from forming; smooth it gently against the surface. Refrigerate pudding for at least 3 to 4 hours before serving.