In a small dry skillet, toast almond slices over low heat five minutes, stirring often. Cool, tip into small bowl, and set aside for garnish.
In a 6-quart covered heavy pot, over medium flame, heat the oil, butter, onions, celery, carrots, wild rice, parsley, thyme, salt, peppers, and asparagus ends (the trimmed bottom third). Let cook about 15 minutes, stirring regularly, until vegetables are softened. Add white wine and garlic; cook 3 minutes or until wine is reduced.
Pour in stock and water; bring to a boil. Reduce heat to a gentle boil and cook 40 minutes or until rice is nearly tender. Remove the asparagus ends and discard. Add the potatoes and the 1/2-inch asparagus pieces. Cover again and cook until potatoes are tender. In the meantime, in a separate small skillet with 1/4 cup water, cook the asparagus tips 2 minutes over medium heat. Drain and rinse in cold water. Set aside in a small bowl for garnish.
Lower heat so that soup isn't simmering at all. Pour in milk, cream, and 2 shakes of hot sauce; stir well. Taste and adjust seasonings. Heat through WITHOUT BOILING. Serve hot garnished with toasted almonds and asparagus tips.
COOK'S NOTE: Easily vegan. Use all olive oil and only vegetable stock.Sub almond or coconut milk for the milk and cream or leave it out all together.