Start by mincing the garlic. If you prefer a deeper, more mellow garlic flavor, sauté it in a small pan with a bit of butter or olive oil over low heat until fragrant.
In a large saucepan or pot, bring the vegetable broth and milk to a gentle simmer over medium heat. Stir occasionally to prevent the milk from scorching.
Once the liquid is simmering, gradually whisk in the cornmeal in a slow, steady stream. Keep whisking continuously to avoid lumps. Once incorporated, lower the heat to medium-low and continue stirring frequently.
Polenta thickens quickly, so keep an eye on it. Stir frequently, using a wooden spoon or whisk, to maintain a smooth consistency. Let it cook for about 20–25 minutes, or until it reaches a creamy, porridge-like texture. If it becomes too thick, add a little extra warm broth or milk to loosen it up.
Once the polenta has reached the desired consistency, stir in the sautéed garlic, butter, parmesan cheese, salt, pepper, and dried thyme. Give the polenta a taste and adjust the seasoning if needed. If you want extra cheesiness, add more parmesan.
Spoon the creamy garlic and parmesan polenta onto plates or into bowls. Garnish with fresh parsley, extra parmesan, and a drizzle of olive oil or melted butter for an extra touch of richness.
