Multi-Mushroom Flatbread Pizza

Ingredients

• 1 1/2 cups warm water, between 100 and 115 degrees F, as measured with a candy thermometer (any hotter will kill the yeast - an organic leavener, too cool and the yeast won't be activated)
• 1 tablespoon salt
• 1 tablespoon sugar
• One 1/4-ounce packet yeast
• 4 cups all-purpose flour, plus some extra for the dough board
• 1/4 cup cornmeal, for pizza stones
• 2 tablespoons butter
• 3 shallots, sliced
• 3 large sprigs fresh thyme, leaves stripped from the stems and minced
• 3 ounces dried porcini mushrooms, soaked in hot water to re-hydrate and remove grit (24 ounces if using fresh)
• Salt and pepper
• 1/2 cup heavy cream
• 2 tablespoons extra-virgin olive oil
• 3 ounces fresh porcini mushrooms, cleaned and trimmed
• 3 ounces fresh cremini mushrooms, cleaned and trimmed
• 3 ounces fresh shiitake mushrooms, cleaned and trimmed
• 2 cloves garlic, lightly crushed with the side of a knife blade, then minced
• 3 large sprigs fresh thyme leaves, stripped from the stems
• 1/2 pound fresh mozzarella cheese, sliced