Prepare the asparagus. Cut off the woody ends. Then cut off the tips and set them aside. Peel the asparagus and chop them on smaller chunks. You can use the woody ends and the peel in vegetable stock, so no need to throw it away.
Blanch the asparagus
Add the asparagus tips to a pot of boiling salted water over medium heat. Cook for about 30 seconds, then remove them from the pot and place under cold running water to stop the cooking process. Drain and set aside.
Place a pot over medium-low heat. Add olive oil, diced onion, and diced garlic cloves. Cook for about 5 minutes, stirring occasionally. Add the chopped asparagus, cayenne pepper, and 1/2 tsp black pepper. Cook for a few minutes, stirring occasionally.
Cook the asparagus soup
Pour the vegetable stock or water to the pot with asparagus. Cook until the asparagus are cooked and soft, for about 5 minutes. Then transfer the soup to a blender or use an immersion blender to blend into a nice, creamy, silky asparagus soup. Check the seasoning and season with salt and pepper.
Divide the soup between two plates. Serve with blanched asparagus tips, a drizzle of olive oil and if you love heavy cream, add a drizzle of heavy cream right before serving. Enjoy. Store any leftovers in a fridge for up to 3 days.