Make the Pesto: In a medium non-stick pan, toast the pine nuts over medium-high heat, stirring continuously for about 2 minutes until golden brown. Remove from heat and let cool. In a blender, combine the chopped cilantro, lemon zest, lemon juice, 1 tsp salt, white sugar, garlic clove, cooled pine nuts, and neutral oil. Blend until smooth. Set aside.
Sauté Aromatics: In a large pot, heat 2 Tablespoons of vegetable oil over high heat. Add the diced onions and cook for 3 minutes. Add the minced garlic and cook for an additional 2 minutes until the onions are translucent.
Simmer the Soup: Use the "bend-and-snap" method to remove the woody ends of your asparagus, then chop the stalks into 1-inch pieces (keeping the tips whole). Add the chopped asparagus, diced potatoes, and 3 tsp of kosher salt to the pot. Sauté for 5 minutes. Pour in the chicken broth and bring to a boil. Reduce the heat to medium-low, cover with a lid, and simmer for 15 minutes.
Blend the Soup: Once the vegetables are soft, use tongs to remove about 12 asparagus tips and set them aside for your garnish. Stir the heavy cream into the pot. Using an immersion blender, carefully purée the soup until completely smooth. (If using a stand blender, work in batches, remove the center cap of the lid, and cover with a towel to allow steam to escape).
Garnish and Serve: Ladle the hot soup into bowls. Drizzle 1 to 2 teaspoons of the Lemon-Cilantro Pesto over the surface and gently place 3 reserved asparagus spears into the center of each bowl. Serve immediately!