Preheat oven to 350 degrees F.
Put the shiitakes into a medium saucepan with cold water to cover. Bring to a boil over medium heat. Reduce the heat and simmer for 15 minutes or until softened. Drain and cool. Remove stems and slice mushrooms 1/4-inch thick. Set aside.
Put the portobellos and white mushrooms in a colander and rinse well.
In a large skillet over medium heat, melt the butter over medium heat. Add the onion and cook until translucent, about 10 minutes. While the onion is cooking, slice the mushrooms and add them to the pan. Add the fresh thyme, dried thyme and dried basil. Season with salt and pepper. Stir well and let cook for 15 minutes or until most of the mushroom liquid has reduced down. Add the shiitakes, red wine and tomato paste and simmer until thickened. Spoon into the partially baked Cornmeal Peppercorn Crust and bake
Place the flour, cornmeal, salt and pepper in a food processor fitted with the steel blade. Pulse until mixed. Cut the butter into small pieces and add to the flour mixture. Pulse until the mix resembles coarse meal. Add the ice water and pulse again until the dough begins to form. Turn out onto a floured surface and knead a few times just to make sure everything is incorporated. Press the dough evenly into the bottom of a 10-inch springform pan and work it up the sides so that you have a 1-inch lip all the way around. Chill the crust for 20 minutes.
Preheat the oven to 375 degrees F.
Line the crust with foil and fill with pie weights, raw rice or dried beans. Bake the crust on the lower rack of the oven for 10 minutes. Very carefully remove the foil and weights and bake another 5 minutes or until the crust is just dry. Remove from the oven and let cool before filling.
Place the heavy cream into the bowl of a mixer and beat at high speed until it begins to thicken. Add the rest of the ingredients and continue to beat until soft peaks form. Serve with tart.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.