To rehydrate the dried porcini mushrooms, place the mushrooms in a medium bowl and cover with boiling water. Let stand for 30 minutes. Once the mushrooms are rehydrated, strain through a fine sieve or a piece of cheesecloth, setting aside the soaking liquid. Set the mushrooms aside.
In a 12- to 14-inch sauté pan, heat the olive oil until hot but not smoking. Add the shallots and garlic and cook over medium heat until slightly soft, about 5 minutes. Add the rehydrated porcini and continue cooking until the onions and garlic begin to color, about 5 more minutes.
Add the fresh mushrooms, turning them with a wooden spoon so they are coated in oil. Allow the mixture to cook until the mushrooms begin to shrink in size, about 8 minutes. Add the reserved porcini soaking liquid and season to taste with salt, pepper and chile flakes. When the mushrooms are tender and the mushroom liquid has reduced to 1/4 cup, remove from the heat. Adjust the seasonings to taste. Stir in the thyme. Let the mushrooms cool. Spread the mushrooms on the rolled-out pizza rounds and sprinkle with the Taleggio cheese before baking.