01 - Preheat oven to 350°F (175°C). Grease a 12-cup muffin tin thoroughly with butter or nonstick spray.
02 - Arrange the sourdough bread cubes evenly on a baking sheet and toast in the oven for 8 to 10 minutes until lightly golden and crisp. Transfer the cubes to a large mixing bowl.
03 - In a large skillet over medium heat, melt 2 tablespoons of butter. Add the chopped onion, celery, and carrots. Cook for 5 to 7 minutes until vegetables are softened. Stir in garlic, sage, parsley, and thyme; cook for 1 minute longer, then remove from heat.
04 - Add the sautéed vegetable mixture to the toasted bread cubes. Season evenly with salt and black pepper, and toss gently to combine.
05 - In a separate bowl, whisk together the eggs, whole milk, remaining 3 tablespoons of melted butter, and vegetable broth until well blended.
06 - Pour the liquid mixture over the bread and vegetables. Gently fold with a spatula until the bread is evenly moistened, being careful not to overmix. Allow the mixture to rest for 5 minutes to absorb moisture. If the mixture appears too dry, add a small amount of additional broth as needed.
07 - Divide the stuffing mixture evenly among the prepared muffin cups, pressing gently with the back of a spoon to compact and shape.
08 - Transfer the muffin tin to the oven and bake for 25 to 30 minutes until the tops are golden and crisp.
09 - Let the muffins cool in the tin for 5 minutes. Carefully remove each portion and serve warm.