How to Make It
Melt 2 tablespoons of the butter in a large, heavy saucepan. Add the white mushrooms and cook over high heat, stirring occasionally, until golden, about 8 minutes. Transfer to a plate.
Melt the remaining 4 tablespoons of butter in the saucepan. Add the onion and shallots and cook over moderate heat until softened. Add the wild mushrooms and cook, stirring occasionally, until tender, about 20 minutes. Add the Cognac and cook until evaporated. Stir in the stock, thyme sprigs, bay leaves and cooked white mushrooms and bring to a simmer. Reduce the heat to moderately low and cook for 45 minutes. Discard the thyme sprigs and bay leaves.
Working in batches, puree the soup in a blender until smooth. Return the soup to the saucepan, stir in the cream and season with salt and pepper.
In a mini food processor, combine the Asiago, cream cheese and egg yolk and pulse until creamy. Spread the Asiago cream on the baguette toasts and arrange on a rimmed baking sheet.
Preheat the broiler. Broil the toasts 8 inches from the heat for about 2 minutes, or until golden and bubbling.
Ladle the soup into shallow bowls and float the Asiago toasts on top. Garnish with the chives and serve.