Preheat oven to 325F.
In a medium skillet, melt butter. Add onions and sauté over medium heat 5 minutes, or until translucent. Add the mushrooms, celery, dill, marjoram, salt, and pepper. Sauté until celery begins to soften.
Place bread cubes in a large bowl. Pour warm onion mixture over bread cubes. Toss to combine.
Add vegetable broth, a little at a time, mixing well, until bread is moist. (The amount of broth used will differ depending on how dry your bread cubes are.) The mixture should be moist, but not soggy, and there should be no water pooling at the bottom of your bowl.
Add the beaten eggs and mix thoroughly.
Distribute stuffing mixture by the ½ cup into greased muffin tins.
Bake for 20 minutes, until the internal temperature reaches 140-160F.