Preheat your oven to 350°F (175°C) and grease a standard muffin tin or line with muffin liners.
In a large mixing bowl, add the cubed bread and set aside.
In a skillet over medium heat, melt the butter. Add the chopped onion and sauté until softened and translucent, about 5 minutes. Add the minced garlic and cook for an additional minute until fragrant.
In a separate bowl, combine the broth, milk, beaten eggs, thyme, rosemary, and black pepper. Whisk until well combined.
Pour the sautéed onion and garlic mixture over the bread cubes, followed by the broth mixture. Gently fold in the cheddar and mozzarella cheeses along with the chopped parsley, ensuring the bread cubes are well coated.
Using a spoon, fill each muffin cup with the stuffing mixture, pressing it down lightly to pack it in.
Sprinkle the grated Parmesan cheese evenly over the top of each muffin.
Place the muffin tin in the preheated oven and bake for 25-30 minutes, or until the tops are golden brown and a toothpick inserted in the center comes out clean.
Allow the muffins to cool for 5 minutes in the pan before transferring to a wire rack. Serve warm and enjoy your cuddly cheesy stuffing muffins!