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Fill a medium sized pot with water and heat on high.
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Peel Sweet Potatoes and cut into medium sized cubes.
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Boil sweet potatoes for 5-7 minutes until tender, but slightly firm.
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Drain and set aside when done.
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Add 2 Tsp. of Olive Oil to a large non-stick skillet on medium/high heat.
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Add walnuts and stir until lightly browned for around 2 minutes.
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Remove nuts, place in a bowl and wipe out the skillet.
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Peel the leaves off the brussel sprouts and discard the cores.
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Add 2 Tsp. of Olive Oil to the same skillet and heat to medium/high.
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Add the garlic and saute for 1 minute.
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Add the brussel sprouts and lemon juice; saute for an additional 2 minutes.
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Add the onion wedges, sweet potatoes, Thyme, salt and pepper to taste.
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Saute for an additional 3 minutes until the onion has softened and potatoes are lightly browned.
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Make room for the eggs by making 3 holes in the hash that are large enough for the eggs to fry on.
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Add the eggs into the holes and cover for around 1 minute until the tops of the eggs are no longer runny.
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Remove from heat and top with toasted walnuts and chunks of goat cheese.