Thinly slice off the top of the tomato using a serrated knife, exposing the core and seeds. Discard the seeds. Using a grapefruit spoon, remove the inside flesh or core of the tomato. Coarsely chop the cores and tops of the tomatoes and set aside. Sprinkle the hollowed out tomatoes with 1/2 teaspoon of the salt and place cut side down on a rack set inside a half sheet pan. Let sit until ready to stuff.
Heat the olive oil in a 12-inch skillet over medium heat. Once the oil shimmers, add the garlic and onion. Cook until the onions are translucent, 2 to 3 minutes. Add the mushrooms and cook for another 4 minutes, stirring occasionally. Add the wine to the pan and cook until most of liquid is absorbed, an additional 4 to 5 minutes. Add the chopped tomato and the panko and cook another 1 to 2 minutes. Add the pinenuts and heat through. Season the mushroom mixture with the remaining salt and the black pepper. Remove from the heat and add the sherry vinegar and 1 tablespoon of the fresh parsley.
Heat the broiler to high and set a rack in the top third of the oven.
Combine the goat cheese and remaining parsley in a small mixing bowl. Stuff each tomato with approximately 1/3 cup of the mushroom mixture. Top each with the goat cheese mixture, dividing evenly among the tomatoes. Place the tomatoes on a half-sheet pan and broil until the cheese is slightly melted and golden, 5 to 7 minutes. Cool slightly before serving.