Simmer the porcini mushrooms and 2 cups water in a saucepan over medium heat. Reduce the heat to low and steep the mushrooms until softened and plump.
In a deep skillet, heat the EVOO, 3 turns of the pan, over medium-high heat. Add the portobello and shiitake mushrooms and cook until tender, about 10 minutes. Season with salt and pepper and the rosemary. Stir in the tomato paste and cook for 1 minute, then stir in the wine and let it cook down, about 1 minute.
Remove the porcini mushrooms from their broth, slice and add to the mushroom gravy. Ladle the porcini broth into the mushroom gravy, leaving any porcini grit in the pan. Adjust the salt and pepper.
Bring a large pot of water to a boil, salt it, add the gnocchi and cook until tender and floating on the surface, about 5 minutes. Drain the gnocchi, add to the mushroom gravy and toss. Serve in shallow bowls, topped with ricotta salata and radicchio.