Procedure:
First of all, prepare the asparagus. Rinse it and pat it dry. Then remove all the 1-inch tips, discarding any bad ones; and set them aside. Then remove the woody portion of the stalks by bending and breaking in the normal way. Discard the woody parts (or let the dogs gnaw on them), and then cut the rest of the stalks into 1-inch pieces.

Melt the butter in the olive oil in a fairly large pot over medium-low heat. Add the chopped onions and cook until tender, about 15 minutes, stirring occasionally. Add the chicken broth and bring to a boil.

Add to the broth the asparagus stalks, carrots, garlic, parsley, tarragon, salt, black pepper and cayenne. Simmer, partially covered, until the vegetables are tender, about 45 to 50 minutes. Remove from heat and let cool.

Using a blender or food processor, liquify the broth and vegetables in batches of 2-3 cups. Strain the soup back into another pot after liquifying. At this point, one can store the soup, covered, in the refrigerator overnight and complete the process later.

Before serving, heat the soup over medium heat. When bubbling, add the asparagus tips, and simmer until the tips are tender and the soup is hot, about 15 minutes. At this point I personally also added the diced tomato. When I tried to dice the tomato, it turned to mush and would not have looked very nice as a garnish.

However, when you serve the soup, you can sprinkle some of the diced tomato on top; and add a dollop of sour cream for added pizazz. I tried the soup with and without the sour cream, and there was little effect on the overall taste and consistency.

This excellent soup can stand on its own without the garnish. It made about 8 servings and is quite filling.