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