Melt the butter in a heavy skillet over moderate heat.
Add the onion and garlic and saute for about 5 minutes, until tender.
Add the remaining ingredients, except the eggs, and bring to a boil.
Reduce the heat and cook covered for 45 minutes, stirring occasionally.
Break the eggs into wells you have made in the hash and cook, covered, an additional 10 to 15 minutes, until the eggs are cooked to the degree you prefer.
Serve immediately.
Notes
Originally from Ireland but more people believe it is American.