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Melt butter in a skillet over medium heat
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Add onion and garlic, and sauté for 5 minutes, stirring occasionally
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Add red and Yukon gold potatoes, rosemary, paprika, salt and pepper and cook until potatoes are soft, stirring occasionally
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Stir in corn and cook until heated through, about 5 minutes
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Press hash into an even layer with spatula and use the back of a spoon to make two 1-inch deep wells into the mixture
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Crack an egg into each well
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Cover skillet and cook until eggs are set, about 5 mintues
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Garnish with fresh green onions.