Soak the porcini in warm water until soft, about 20 minutes. Squeeze the soaked porcini, and slice them into ¼-inch-wide pieces. Strain the soaking water through a cheesecloth or coffee filter into a bowl. Keep this mushroom water warm.

Place the olive oil in a large pan over medium heat. Add the onions. Season lightly with salt, and stir to combine. Slowly raise the heat until the onions are sizzling, and cook, stirring frequently, until the onions are soft and shiny but not browned, about 6 minutes.

Add the dried and fresh mushrooms to the skillet with the onions, and toss to combine. Sprinkle with a small amount of additional salt; add the thyme and rosemary toss briefly, raising the heat a bit; and cover the pan. Cook about 3 minutes (tip: shake the skillet now and then to move the mushrooms). Uncover the skillet, and continue to cook over medium-high heat, stirring frequently, as the mushrooms shrink and the liquid evaporates, about 5 more minutes. When the liquid has evaporated and the mushrooms begin to brown, clear a spot in the pan, drop in the tomato paste, and cook, stirring, for 1 minute. When the vegetable mixture is sizzling and browning again, add the wine to the skillet. Stir constantly as the wine thickens and evaporates.

When the mushrooms are almost ready, cut the polenta into rectangles or triangles, brush lightly with olive oil, and place on a hot grill pan, turning once with tongs until the grilled polenta crisp and seared with grill marks, 4 to 5 minutes per side.

To plate the dish, place the grilled polenta on individual serving plates, top with the warm mushrooms, sprinkle on the minced parsley, grated parmesan and serve warm.