Peel the lower third of the asparagus stalks, and discard the trimmings. Cut the asparagus on the bias into slices about 1/4 to 1/2-inch thick. (You should have about 1 1/2 cups.) Bring 1/2 cup of the water to a boil in a saucepan, and add the asparagus pieces. Bring the water back to a boil, and boil the asparagus for 30 seconds. Drain, reserving the cooking juices, and set the cooked asparagus pieces aside in a bowl.
Place the yellow peppers, potato, onion, garlic, salt, sugar, and pepper in a large saucepan, and add the remaining 2 cups of water. Bring to a boil, add the reserved asparagus cooking juices, cover, and reduce the heat to medium. Cook the mixture for 30 minutes, then push it through a food mill fitted with a fine screen to remove the skin of the yellow peppers.
Add the butter and oil, and emulsify the mixture with a handheld immersion blender until it is smooth and creamy in appearance. Add the reserved asparagus, heat through, and serve
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