1 stalk green garlic, white parts only, thinly sliced
2 tbsp evoo, plus 2 tsp, separated
1 to 1 1/2 lbs (thin to medium) asparagus, trimmed and cut on the diagonal into 2-inch lengths
Heat the evoo over moderately high heat in a large, heavy skillet. Add the asparagus. Saute until the asparagus is tender and the skin has shriveled slightly, about five minutes. Add the garlic, and continue to saute for another minute until the garlic is translucent. Season to taste with s&p. Drizzle with basil evoo. Toss to combine.
Meanwhile, heat remaining 2 tsp evoo in a medium nonstick skillet over moderate heat. Gently crack eggs into the skillet. Season eggs lightly with s&p. Cook until the whites are just set and the yolks are still runny, about 2 minutes.
Serve asparagus topped with fried eggs.