Sprinkle the mushrooms with lemon juice to prevent them from turning brown and set them aside.
In a large saucepan, melt the butter over medium heat and sauté the shallots until they are soft and translucent.
Add the mushrooms, thyme, and bay leaf to the saucepan and cook, stirring frequently, until the liquid evaporates.
This should take about 10 minutes.
Pour in the heavy cream and chicken broth, stirring the mixture well.
Bring it to a simmer and let it cook for about 20 minutes.
Dissolve the cornstarch in a little water, then stir it into the soup to thicken.
Cook for an additional 5 minutes, seasoning with salt and pepper to taste.