Adjust oven rack to middle and lower-middle positions; heat oven to 400 degrees.
Melt 8 tablespoons of the butter (1 stick) in a 12-inch skillet over medium-high heat. Add the celery and onion and sauté until softened, 6 to 8 minutes. Stir in the parsley flakes, poultry seasoning, pepper, and salt, and cook for 30 seconds more until fragrant.
Transfer the vegetable mixture to a large mixing bowl. Add the toasted bread cubes to the bowl and toss to combine.
Whisk the milk, water, and chicken base together in a large glass measuring cup. Pour the liquid mixture over the bread and veggie mixture and use a rubber spatula to fold everything together until evenly combined. Allow the mixture to sit for about 10 minutes, and then fold the mixture together again to ensure the liquid is fully absorbed.
Spray two 12-cup muffin pans with non-stick spray. Divide the stuffing mixture evenly among 18 muffins cups. Gently press on the tops to fill the cups and pile more on top to form a loose dome shape.
Melt the remaining 4 tablespoons of butter in the microwave, and brush it over the tops of the stuffing muffins.
Bake at 400 degrees until the tops of the muffins and browned and crispy, about 35 minutes. Rotate the muffin tins midway through baking.
Cool the stuffing muffins in the muffin tins on a wire rack for 15 minutes. Then transfer the muffins to a wire rack and allow them to rest for another 10 minutes before serving.
Recipe Notes
To make ahead: Cooled muffins can be stored in an airtight container in the refrigerator for up to 2 days or in the freezer for up to one month.Reheating: Thaw in the refrigerator overnight. Bake refrigerated or thawed frozen muffins on a rimmed baking sheet at 350 degrees until heated through.