Warm broth and milk in a medium saucepan over medium heat. Stir in garlic and salt; bring to a gentle simmer.
Whisk in the cornmeal in a slow, steady stream to prevent lumps.
Reduce heat to low. Cook, whisking often at first, then stirring, until thick and tender, 25–30 minutes.
Take off heat. Stir in butter, Parmesan, and heavy cream until smooth and glossy.
Season with pepper and more salt if needed. Thin with a splash of hot milk or broth if too thick.
Serve right away while creamy; polenta will firm as it cools.