Warm 2 cups of the chicken broth. Put the porcini into a heatproof bowl, add the warm stock, and let stand for 20 minutes. Transfer the porcini to a cutting board and chop. Strain the broth into a bowl and set aside.

In a large wide pot or deep sauté pan, over medium heat, melt the butter. Add the shallots and a pinch of salt and sauté until soft, about 3 minutes. Add the porcini and cremini mushrooms and the garlic and cook, stirring, until the mushrooms are tender, about 5 minutes.

Add the sherry and simmer for 1 minute. Stir in the flour. Slowly add the mushroom soaking liquid and the remaining 2 cups stock, stirring until combined. Reduce the heat to low and simmer, stirring occasionally, for about 20 minutes. Add the cream.

Working in batches, puree the soup in a blender until smooth, then return the soup to the pot. Season with salt and pepper. Re-warm over low heat until warm, then serve.