In a large saute pan, heat butter on medium and add garlic and onion and cook for 2 - 3 minutes.
Stir and add potatoes and turn heat up to medium to high. Stir occasionally so the potatoes and onions don't burn, but not too much so the potatoes can get a nice crisp edge. Salt and pepper to taste.
When potatoes are almost done, add peppers and sausage and cook for another couple of minutes until sausage is heated and peppers are cooked but still a bit crunchy. Add more salt and pepper if needed.
Meanwhile, put water on to boil for poached eggs. Or cook eggs any other way preferred - sunny side up, fried, etc.
Add cheese to pan with potatoes and remove pan from heat.
One water has begun to boil, poach eggs by breaking eggs one at a time into sieve over a large bowl and give them a litte shake. Add sieve to the boiling water and use a slotted spoon to gently form whites around the egg and then turn sieve to drop egg into the water. Repeat with other eggs.
Mx hash with melted cheese, plate, top with eggs, and serve!