In a large Dutch oven or heavy pot, melt butter and olive oil together over medium heat. Add leeks, shallots and onions and stir to combine and coat with melted butter. Season with salt and pepper. Reduce heat to medium and cook until vegetables are softened, stirring frequently, about 10-15 minutes.
Increase heat to high and add chicken broth, cubed potatoes and bay leaves. Bring mixture to a boil, reduce heat and simmer until the potatoes are soft and tender, about 12-15 minutes. Remove half the potatoes and set aside. Add toasted bread and cook until bread begins to dissolve, about 5 more minutes. Remove bay leaves. Puree soup until smooth using a blender or food processor. Stir in reserved potatoes and evaporated milk. Top with Tangy Tarragon Drizzle before serving.
Mix all ingredients in a medium bowl. Season with salt and pepper. May be covered and refrigerated until ready to use. To serve, drizzle on soup and garnish with tarragon leaves.
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