In a large saute pan, heat olive oil over medium heat. Add shallots and cook until they begin to soften. Add mushrooms, thyme and sherry. Cook until mushrooms are tender, 8 - 10 minutes. Season to taste with salt and pepper. Drain mushrooms and reserve.
Place chicken broth in a medium saucepan. Combine cornstarch and water to make a smooth paste. Stir into chicken broth and bring to a boil over medium heat, stirring constantly. Remove from heat. Stir in lemon and lime juices and sour cream. Season to taste with salt and pepper. Keep warm but do not allow to return to a boil. (I put the saucepan in a larger one with simmering water).
Preheat oven to 400°F Soften corn tortillas by gently frying in a small amount of hot oil: drain excess oil. Do not allow tortillas to crisp. (I steam them in the microwave with a little water for fewer calories).
Divide mushroom mixture into 8 portions and place in center of softened tortillas. Roll each tortilla jellyroll-style and place seamside down, sides touching, in an ovenproof baking dish.
Pour sour cream sauce over inchiladas and top with grated cheese. Bake 10 minutes. Makes 4 servings.