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Melt butter with olive oil in a large soup pot. Add fennel, leeks and onion to the butter/olive oil mixture. Prepare asparagus by breaking off the tough bottoms and then chopping the usable asparagus into 1/2-inch pieces. Add asparagus to the soup pot. Sauté the vegetables for 20 minutes until they are tender. Stir the vegetables occasionally.
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Add white rice to the cooked vegetables along with vegetable stock, thyme bundle, 2 T. salt and 1 t. pepper. Bring the soup mixture to a boil and then lower heat and simmer the soup for 30 minutes. This mixture will be done when the rice is very tender. Take the soup off the heat, remove and discard the thyme bundle,and stir in basil and Pernod.
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Meanwhile, boil a small amount of water in a separate pan and cook asparagus tips for about 2 minutes or until they are just tender. You will use the tips as garnish for your finished soup. When the asparagus tips are done, remove them from the hot water, drain them and transfer them to a bowl of ice water. Set aside until you are ready to serve the soup.
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Puree the soup mixture in a blender. Add the half-and-half and adjust seasonings.
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Ladle the hot soup into individual bowls. Sprinkle with a generous pinch of parmesan and garnish with julienned basil, an asparagus tip and a small pinch of either paprika or cayenne pepper. I also garnished the soup with a small whole basil leaf.