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Heat 1 Tbsp. peanut oil in a medium skillet over medium heat.
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Add sweet potatoes and carrots and saute until just starting to often, about five minutes.
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Next, add curry paste, garlic cloves, and ginger and saute until fragrant, thirty seconds.
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Add brown sugar and saute for another 15 seconds and or until melted.
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Add garlic sauce, coconut milk, and water.
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Raise heat to medium-high and bring to a simmer. Let simmer for 10 minutes or until the sweet potatoes are easily pierced with a fork.
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Add ramen and peas and cook for another 3 minutes. Remove from heat, squeeze in lime juice, and set aside.
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Heat the remaining 1 Tbsp. peanut oil in a small skillet over medium heat. Once oil is hot but not smoking, add asparagus and ramps and saute until starting to brown on all sides, about 5 to 7 minutes. Remove from heat and set aside.
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To soft boil the eggs: Place two eggs in a small saucepan and cover with enough water to completely cover the eggs. Transfer to stove top and heat over high until boiling. Let boil for one minute and then remove from heat. Cover and let sit for six minutes. Run eggs until cold water for three minutes. Peel eggs and sliced in half.
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Divide the ramen mixture between two large soup bowls and divide the asparagus, ramps, eggs, scallions, radish, and basil between the bowls. Sprinkle with sesame seeds. Serve right away.