Cut or break off asparagus tips, about 3 inches in length, and set aside. Chop remaining parts of asparagus spears into ½ inch pieces and set aside.
Melt butter over medium high heat in deep pot. Add asparagus tips and toss around in butter for about 90 seconds. Remove to a plate using a slotted spoon and reserve for garnish.
Add chopped shallots to butter and lower heat to medium. Cook about 5 minutes, until the shallots are translucent, stirring frequently.
Add the parsley and stir for about 30 seconds.
Add the potatoes and stir well. Pour in the chicken broth, turn heat up to high and bring to a boil.
When the broth is boiling, add the ½-inch asparagus stalk pieces. Lower the heat to simmer, partially cover the pot, and cook for 20-30 minutes, or until the asparagus stalk pieces and potatoes are very tender.
Add the spinach, stir to submerge the leaves, cover the pot partially and simmer 5 minutes.
Using an immersion blender, carefully blend soup until it is a smooth consistency. (Or carefully transfer portions of the soup to a blender to puree until smooth.)
Add whipping cream and stir well to combine.
Add juice of one lemon to the soup. Salt and pepper the soup to taste.