In a deep bowl, use a hand mixer or a sturdy whisk to cream the softened butter until it's light and fluffy.
Beat in the eggs one at a time until fully incorporated.
Add about a third of the flour, followed by half of the milk, beating gently after each addition.
Repeat this process, alternating between the flour and milk, until everything is combined. Be careful not to overmix.
Gently fold in the salt, nutmeg, and cayenne pepper. The final batter should be smooth, creamy, and hold its shape on a spoon.
Bring a large pot of heavily salted water or your desired soup broth to a gentle boil.
Drop the dough by ½ teaspoonfuls directly into the simmering liquid.
Don't overcrowd the pot; cook in batches if necessary.
Cover the pot and let the dumplings simmer for about 15 minutes, or until they are puffed up and cooked through. Use a slotted spoon to gently remove them and add them directly to your soup bowls for serving.
Do not overmix the batter once the flour is added.
Mix only until the are just combined to avoid developing gluten, which can make the dumplings tough.